E7
10.29
lATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM REPORT
DIGITAL-COMPUTER-CONTROLLED * TRAFFIC SIGNAL SYSTEM I FOR A SMALL CITY
NAS-NRC
UBRARY
IIGHWAY RESEARCH BOARD lATIONAL RESEARCH COUNCIL lATIONAL ACADEMY OF SCIENCES-NATIONAL ACADEMY OF ENGINEERINQ HIGHWAY RESEARCH BOARD 1966
Officers J. B. McMORRAN, Chairman EDWARD G. WETZEL, Firsl Vice Chairman DAVID H. STEVENS, Second Vice Chairman W. N. CAREY, JR., Executive Director
Executive Committee REX M. WHITTON, Federal Highway Administrator, Bureau of Public Roads (ex officio) A. E. JOHNSON, Executive Secretary, American Association of State Highway Officials (ex officio) JOHN C. KOHL, Executive Secretary, Division of Engineering, National Research Council (ex officio) WILBUR S. SMITH, Wilbur Smith and Associates (ex officio. Past Chairman 1964) DONALD S. BERRY, Chairman, Department of Civil Engineering, Northwestern University (ex officio, Past Chairman 1965) E. W. BAUMAN, Managing Director, National Stag Association MASON A. BUTCHER, County Manager, Montgomery County, Md. J. DOUGLAS CARROLL, JR., Executive Director, Tri-Stale Transportation Committee, New York City C. D. CURTISS, Special Assistant to the Executive Vice President, American Road Builders' Association HARMER E. DAVIS, Director, Institute of Transportation and Traffic Engineering, University of California DUKE W. DUNBAR, Attorney General of Colorado i JOHN T. HOWARD, Head, Department of City and Regional Planning, Massachusetts Institute of Technology EUGENE M. JOHNSON, Chief Engineer, Mississippi Slate Highway Department PYKE JOHNSON, Retired LOUIS C. LUNDSTROM, Director, Automotive Safety Engineering, General Motors Technical Center, Warren, Mich. BURTON W. MARSH, Executive Director, Foundation for Traffic Safety, American Automobile Association OSCAR T. MARZKE, Vice President, Fundamental Research, U. S. Steel Corporation J. B. McMORRAN, Superintendent of Public Works, New York State Department of Public Works i CLIFFORD F. RASSWEILER, President, Rassweiler Consultants, Short Hills, NJ. \ T. E. SHELBURNE, Director of Research, Virginia Deparlmeiu of Highways DAVID H. STEVENS, Chairman, Maine State Highway Commission JOHN H. SWANBERG, Chief Engineer, Minnesota Department of Highways EDWARD G. WETZEL, The Port of New York Authority, New York City J. C. WOMACK, State Highway Engineer, California Division of Highways K. B. WOODS, Goss Professor of Engineering, School of Civil Engineering, Purdue University
NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM Advisory Committee J. B. McMORRAN, New York State Department of Public Works, Chairman DONALD S. BERRY, Northwestern University A. E. JOHNSON, American Association of State Highway Officials JOHN C. KOHL, National Research Council DAVID H. STEVENS, Maine Slate Highway Commission EDWARD G. WETZEL, The Port of New York Authority REX M. WHITTON, Bureau of Public Roads
Advisory Panel on Traffic ALGER F. MALO, City of Detroit, Chairman HAROLD L. MICHAEL, Purdue University EDWARD A. MUELLER, Highway Research Board
Section on Operations and Control (FY '63 and FY '64 Register) JOHN E. BAERWALD, University of Illinois RAY W. BURGESS, Louisiana Department of Highways (Resigned 1964) RICHARD C. HOPKINS, Bureau of Public Roads FRED W. HURD, Yale University CHARLES J. KEESE, Texas A&M University KENNETH G. McWANE, Highway Research Board (Resigned 1964) KARL MOSKOWITZ, California Division of Highways O. K. NORMANN, Bureau of Public Roads (Deceased) FLETCHER N. PLATT, Ford Motor Company E. S. PRESTON, Ohio Department of Highways (Resigned 1963) CARLTON C. ROBINSON, Automotive Safety Foundation (Resigned 1964) DAVID W. SCHOPPERT, Automotive Safety Foundation (Resigned 1963) W. T. TAYLOR, JR., Louisiana Department of Highways (Resigned 1964)
Program Staff W. A. GOODWIN, Program Engineer K. W. HENDERSON, JR., Assistant Program Engineer H. H. BISSELL, Projects Engineer L. F. SPAINE, Projects Engineer W. L. WILLIAMS, Assistant Projects Engineer HERBERT P. ORLAND, Editor M. EARL CAMPBELL, Advisor NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM REPORT
^GITAL-COMPUTER-CONTROLLED TRAFFIC SIGNAL SYSTEM FOR A SMALL CITY
MORTON I. WEINBERG, HARVEY GOLDSTEIN, TERENCE J. MCDADE, AND ROBERT H. WAHLEN CORNELL AERONAUTICAL LABORATORY BUFFALO, NEW YORK
RESEARCH SPONSORED BY THE AMERICAN ASSOCIATION
OF STATE HIGHWAY OFFICIALS IN COOPERATION
WITH THE BUREAU OF PUBLIC ROADS
SUBJECT CLASSIFICATION:
TRAFFIC CONTROL AND OPERATIONS
TRAFFIC FLOW
TRAFFIC MEASUREMENTS
HIGHWAY RESEARCH BOARD DIVISION OF ENGINEERING NATIONAL RESEARCH COUNCIL NATIONAL ACADEMY OF SCIENCES-NATIONAL ACADEMY OF ENGINEERING 1966 NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM
Systematic, well-designed research provides the most effective approach to the solution of many problems facing highway admmistrators and engineers. Often, highway problems are of local interest and can best be studied by highway departments individually or in cooperation with their state universities and others. However, the accelerat• ing growth of highway transportation develops increasingly complex problems of wide interest to highway authorities. These problems are best studied through a coordinated program of cooperative research.
In recognition of these needs, the highway administrators of the American Association of State Highway Officials initiated in 1962 an objective national highway research program employing modern scientific techniques. This program is supported on a continuing basis by Highway Planning and Research funds from participating member states of the Association and it receives the full cooperation and support of the Bureau of Public Roads, United States Department of Commerce.
The Highway Research Board of the National Academy of Sciences-National Research Council was requested by the Association to administer the research program because of the Board's recognized objectivity and understanding of modern research practices. The Board is uniquely suited for this purpose as: it maintains an extensive committee structure from which authorities on any highway transpor• tation subject may be drawn; it possesses avenues of com• munications and cooperation with federal, state, and local governmental agencies, universities, and industry; its rela• tionship to its parent organization, the National Academy of Sciences, a private, non-profit institution, is an insurance of objectivity; it maintains a full-time research correlation staff of specialists in highway transportation matters to bring the findings of research directly to those who are in a position to use them. This report is one of a series of reports issued from a continuing The program is developed on the basis of research needs research program conducted under a three-way agreement entered into in June 1962 by and among the National Academy of Sciences- identified by chief administrators of the highway depart• National Research Council, the American Association of State High• ments and by committees of AASHO. Each year, specific way Officials, and the U. S. Bureau of Public Roads. Individual fiscal agreements are executed annually by the Academy-Research Council, areas of research needs to be included in the program are the Bureau of Public Roads, and participating state highway depart• proposed to the Academy and the Board by the American ments, members of the American Association of State Highway Officials. Association of State Highway Officials. Research projects to fulfill these needs are defined by the Board, and qualified This report was prepared by the contracting research agency. It has been reviewed by the appropriate Advisory Panel for clarity, docu• research agencies are selected from those that have sub• mentation, and fulfillment of the contract. It has been accepted by mitted proposals. Administration and surveillance of re• the Highway Research Board and published in the interest of an effectual dissemination of findings and their application in the for• search contracts are responsibilities of the Academy and mulation of policies, procedures, and practices in the subject problem its Highway Research Board. area.
The needs for highway research are many, and the The opinions and conclusions expressed or implied in these reports are those of the research agencies that performed the research. They National Cooperative Highway Research Program can are not necessarily those of the Highway Research Board, the Na• make significant contributions to the solution of highway tional Academy of Sciences, the Bureau of Public Roads, the Ameri• can Association of State Highway Officials, nor of the individual transportation problems of mutual concern to many re• states participating in the Program. sponsible groups. The program, however, is intended to NCHRP Project 3-2 FY'63 complement rather than to substitute for or duplicate other NAS-NRC Publication 1474 highway research programs. Library of Congress Catalog Card Number: 66-62659 FOREWORD This final report will be of special interest to traffic engineers and highway officials responsible for efficient operation of the existing urban street complex. It is an By Staff aggregation of current methods, equipment requirements, and costs for a computer- controlled traffic signal system. Instrumentation requirements for a real-time Highway Research Board computer system for a small city are presented, and guidelines are developed to aid engineers in selecting control equipment. Control logic to be utilized by the computer in making signal change decisions is included. An annotated bibliography of previously completed research is contained in the appendix.
This investigation stems from the NCHRP project entitled "Surveillance Methods and Ways and Means of Communicating with Drivers." Only the findings of this project that pertain to traffic signal systems are reported herein. Studies involving freeway surveillance and the airborne observer in traffic control are presented in NCHRP Report No. 28. As the traffic demand on the urban street system grows, the need for safe and efficient traffic signal timing continuously increases. In many urban areas severe traffic congestion has developed and new methods of alleviating the situation are desired. One approach that seems likely to ease the congestion problem is the utilization of a real-time digital-computer-controlled traffic signal system. Further• more, due to the recent technological advancements in computer equipment, this type of traffic control, once considered exotic, seems likely to become in the near future a realistic alternative to be considered in the design and modernization of improved signal systems. For these reasons this research was conducted to apply state-of-the-art computer technology to traffic signal control, with emphasis being placed on applications for the small or medium-size city. This research presents the most comprehensive analysis of control logic known to date coupled with a synthesis of the hardware required for a real-time closed-loop digital-computer-controlled traffic signal system. Although the system is based on a theoretical analysis, this report should extensively aid cities that are planning and developing digital-computer-controlled signal systems. It is highly desirable that the principles presented be applied to a real traffic system to validate this research.
The city of White Plains, N. Y., with a population of 50,000 and a trade area serving more than 250,000, was selected as a typical city to study. Utilizing this city as a model, a typical computer signal system is specified, equipment is selected, and costs are estimated for its 116 signalized intersections. Based on the analysis presented, it is anticipated that computer control requirements and costs may be estimated for other typical cities in this population class. Control logic is derived based on the theories of minimum aggregate delay. The equations are presented in a readily usable form for solution by a computer system that is sensing traffic and making control decisions in real time. The report also provides needed information pertaining to acceptable criteria for the design and placement of traffic sensing devices. In the control scheme presented, the signal change decisions are based on comparisons of time savings expressed in terms of relative delay and computer- derived predictions of future delays that will be incurred throughout the signalized network. In the event that street traffic is controlled utilizing the strategy presented, it is likely that major savings in time can be gained by the motorist traveling within the network of signalized intersections. CONTENTS
1 SUMMARY
2 CHAPTER ONE Introduction
2 CHAPTER TWO Synthesis of a Digital-Computer-Controlled Traffic Signal System Definitions and Nomenclature Mathematical Model Measured Traffic Quantities Predictions Application to a City Available Computer Systems Additional Utilization of Computing System Instrumentation System Instrumentation Cost Concluding Remarks
20 REFERENCES
21 APPENDIX A Vehicle Detectors and Their Locations for Surveillance of Traffic in a Street Network
25 APPENDIX B An Estimate of Traffic Surveillance and Signal State Data for a Digital-Computer-Controlled Traffic Signal System
31 APPENDIX c Input Instrumentation Requirements for a Real- Time Digital-Computer-Controlled Traffic Signal System.
37 APPENDIX D Derivation of a Minimum-Delay Function for an Isolated Intersection with Simplifying Assumptions
42 APPENDIX E Derivation of a Minimum-Delay Function for a Subnetwork of Signalized Intersections
52 APPENDIX I- Criteria for Selection of the Digital Computer
59 APPENDIX G Implementation and Prediction Techniques as Applied to the Subnetwork Equations
67 APPENDIX H Applications of the High-Speed Digital Computer in Control of Traffic
76 APPENDIX I Annotated Bibliography FIGURES 3 Figure 1. Adaptive-control feedback loop. 5 Figure 2. Events within a A/ interval during the ^GIK.W, 0KIX,« phase. 7 Figure 3. Queue length vs time. 7 Figure 4. Intersection of two one-way streets. 8 Figure 5. Subnetwork (q, r, s, t, u) of signalized intersections. 10 Figure 6. Descriptive flow chart of the implemented criterion. 11 Figure 7. General flow chart of saving and delay equation criterion. 12 Figure 8. Integrated control system, both central site and street network. 13 Figure 9. Updating prediction technique. 14 Figure 10. Locations of signalized intersections in White Plains, N.Y. 15 Figure 11. Input data format. 15 Figure 12. Output data format. 17 Figure 13. Intersection configuration. 18 Figure 14. Monitor for phase condition of signal controller. 19 Figure 15. Computer central site input control logic diagram. 19 Figure 16. Computer central site output control logic diagram. 23 Figure A-1. Detectors at stop line. 23 Figure A-2. Mid-block detector. 24 Figure A-3. Stop-line and departure detectors. 26 Figure B-1. Analog trace from loop detector. 27 Figure B-2. Single loop, two traffic lanes. 27 Figure B-3. Analog trace and time derivative. 29 Figure B-4. 29 Figure B-5. 32 Figure C-1. Intersection configuration. 33 Figure C-2. Time-sharing vehicle pickups using signal controller phase as gate. 34 Figure C-3. Suggested hardware for time-sharing vehicle detector units at intersection. 35 Figure C-4. Monitor for phase condition of signal controller. 35 Figure C-5. Central site input logic. (D,, Ds, . . ., DN represent the possible eight detectors located at an intersection.)
36 Figure C-6. Computer central site input control logic diagram. 36 Figure C-7. Computer central site output control logic diagram. 38 Figure D-1. Traffic control loop logic flow diagram. 40 Figure D-2. 43 Figure E-1. Intersection of two one-way streets. 43 Figure E-2. Subnetwork (q, r, s, t, u) of signalized intersections. 46 Figure E-3. Prediction of length of queue at point 2 (west leg) 6/K»,K seconds after decision to extend ^niis.w. 46 Figure E-4. Prediction of length of queue at point 2 (west leg) feVK'.„„ seconds after start of deferred ^OIK.W. 53 Figure F-1. Input data format. 53 Figure F-2. Typical detector locations at an intersection. 53 Figure F-3. Output data format. 54 Figure F-4. Bit configuration for a vehicle presence at each detector. 56 Figure F-5. General flow chart of saving and delay equation criterion. 63 Figure G-1. Arrivals to q from s. 65 Figure G-2. Intersection pair q,s. 66 Figure G-3. Time series of signal cycles at intersection q. 68 Figure H-1. Orthogonal signalized intersection of two 2-lane, two-way streets. 69 Figure H-2. Traffic parameters per approach lane. 70 Figure H-3. Role of simulation in real-time control of traffic signals. 71 Figure H-4. Two-phase semi-vehicle-actuated controller. 73 Figure H-5. Two-phase full-vehicle-actuated controller. 75 Figure H-6. Progressive mode; selection of offset and cycle length.
TABLES 50 Table E-1. Application of Derived Equations to Various Signal States at q. 53 Table F-1. Signal States and Coding. 54 Table F-2. Coded Combination of Detectors. 57 Table F-3. Analysis of Signalized Intersections of Typical City by Type, Distribution, and Computer Cycles Required. 58 Table F-4. Cost Analysis for a Single-Processor Computing System, System A. 58 Table F-5. Cost Analysis for a Two-Processor Computing System, System B. ACKNOWLEDGMENTS
Morton I. Weinberg, Head, Transportation Systems Section, the digital computer system as necessary to determine capacity had primary responsibility for the technical direction and and compute speed. He also investigated and selected typical administration of the project reported in both this report and digital computers that could be used for the network control NCHRP Report 28. Other Cornell Aeronautical Laboratory system defined in Chapter Two, and had co-responsibility for staff personnel working on the portions of the project reported Appendix F. herein were as follows: John P. Persico, Associate Mathematician, who conducted all data reduction runs and assisted in the model derivations and Harvey Goldstein, Associate Electronics Engineer, who con• development. ducted and performed the detailed investigation into control Appreciation is expressed to the several individuals and com• techniques and philosophies applicable to the digital-computer- panies who provided the project team with valuable assistance. controlled traffic signal network, including the development of Special acknowledgment is given to the following: the control equations and statistical processes used therein, and assisted in determining some of the requirements for traffic J. T. Hewton, Traffic Engineer, The Municipality of Metro• surveillance equipment for this system. He was primarily re• politan Toronto, for information on the equipment and progress sponsible for Appendices E, G, H, and I, and had co-responsi• of the computer-controlled traffic signal system in Toronto. bility for Appendix F. Roy A. Flynt, Commissioner of Planning, and Robert A. Terence J. McDade, Research Electronics Engineer, who MacMonigle, (formerly) Traffic Engineer, both of the City of performed the investigation into equipment necessary to bring White Plains, N. Y., for traffic data with which to construct a traffic surveillance information into the digital computer and to traffic model. implement the signal control commands. He was primarily Sherwood B. Bliss, Account Representative, International responsible for Appendix C. Business Machines Company, and Gary D. Haynes, Sales Robert H. Wahlen, Associate Electrical Engineer, who Engineer, Sperry-Rand Corporation, for information on their programmed portions of the control equations developed for respective company's computer characteristics. DIGITAL-COMPUTER-CONTROLLED TRAFFIC SIGNAL SYSTEM FOR A SMALL CITY
SUMMARY This study is concerned with research on traffic control systems for an urban street complex. The present report describes the manner in which a control doctrine was developed and a digital-computer-controlled traffic signal system was synthesized for a small city. Equations were developed for assignment of right-of-way at an intersection that would result in minimum aggregate delay to motorists, within certain constraints. The equations are intended for solution in real time, using current information on traffic behavior within the street network. Traffic surveil• lance is to be accomplished by means of in-pavement loop detectors. Traffic and signal state information are transmitted to the central computer site via voice-grade telephone lines. A high-speed general purpose digital computer is to be used for processing the incoming data and "deciding" when commands to the signals to change phase should be generated. Changing of signal phase would be done by a pulse from the computer output acting on the local controller, which would be selected to act in the manual mode. The evaluation of delay at an intersection is extended to include a subnetwork of not more than five intersections, the one being evaluated and the four downstream along the departure legs. This is typical of the intersection of two two-way streets. The City of White Plains, N. Y., was selected as a traffic model. With a popula• tion of 50,000 acting as the core of a mercantile center serving 250,000, White Plains has 116 signalized intersections, for which it was estimated that 464 detectors would be needed to keep the computer adequately informed. The minimum delay function was programmed in FORTRAN IV language, along with the subroutines for evaluation of quantities to be predicted, constants, and other inputs. In determining the storage capacity and computing speed requirements for the machine, all intersections were given an equal weight of importance. That is, it was assumed that a decision might be needed at each intersection at the end of each computing interval. The latter was assumed to be 2 sec, which is estimated to be adequate for real-time changes in the traffic complex. From the calculated computing machine requirements, two systems were selected from currently available equipment. The two had different purchase prices and maintenance charges, but over a 5i-year period either would have cost about $445,000, or $6,740 per month. It was estimated that programming and debugging the traffic control logic in the machine would cost about $25,000. Detectors, tone generators, revisions to the local controllers, decoders, and input- output interface equipment at the computer were assembled into an inventory estimated to cost $229,000. Voice-grade telephone lines are expected to be used for communication of traffic data, signal states, and phase change commands. The rental fee for these lines was estimated to cost $2,000 per month. Finally, it is suggested that the digital computer can be used for other purposes when the traffic load is light enough that the local controllers will give adequate service. At these times the computer will command the local controllers to take over so that it can be used as a business machine to serve the city's business and adminis• tration computing needs. CHAPTER ONE
INTRODUCTION
The foreword of NCHRP Report No. 9 (/) closed with nished a fairly complete traffic model. A control doctrine ". . . The next phase will include a study of freeway sur• of minimum delay was adopted and a generalized expres• veillance, a study of a digital-computer-controlled traffic sion was developed to evaluate delay for a subnetwork of signal network, further study of the requirements of an intersections. This, and the manner in which the expres• airborne-observer surveillance and control system, and a sions were implemented for real-time solution on a high• study of driver communication by aural and visual mes• speed digital machine, is the subject matter of this report. sages." Of the four tasks named, only the last has not been In addition, an inventory of surveillance and communica• pursued. The results of the studies involving freeway sur• tions equipment has been synthesized and the cost of the veillance and the airborne observer are presented in whole system, apart from the traffic signals and local con• NCHRP Report No. 28 (2). trollers, has been estimated. The current report deals with the digital-computer-con• This research presents to the traffic engineer an idea of trolled traffic signal network study. The approach that has what and how many dollars, is involved in implementing a been taken is to synthesize this type of signal system for a digital-computer control system for medium and small small city. A typical small city. White Plains, N. Y., fur• cities.
CHAPTER TWO
SYNTHESIS OF A DIGITAL-COMPUTER-CONTROLLED TRAFFIC SIGNAL SYSTEM
Traffic signals are generally employed at intersections as reduction of the avoidable delay. The values of the control control devices, to alternately assign the right-of-way to parameters selected (cycle length, splits, etc.) are at times orthogonally opposed traffic flows. However, determina• critical if service to motorists is to be optimized. The term tion of the apportionment of the total available time that is optimization in this context is used to mean the minimiza• assigned to each flow or traffic movement will be a function tion of the motorists' travel time or delay. of the type of control used and the predetermined criterion, By its very nature vehicular traffic is widely variable, with or set of criteria, it is to implement. The selection of these random fluctuations superimposed on regular hourly, daily, criteria, or the figure-of-merit which is used to determine weekly and seasonal patterns. Therefore, the limitations of the operational effectiveness of the particular control, is in pretimed control of traffic signals are obvious. Hence, itself open to further commentary and research. That is, there have been numerous attempts to make the signal con• although most consideration has been given to the physical trols of both networks and isolated intersections sensitive problem, many unknowns exist concerning the psycholog• to traffic fluctuations. As a consequence, there are many ical stimuli to the human driver and their particular effect types of specialized traffic signal equipment and systems on his performance (e.g., accident proneness). In the study (traffic-actuated and traffic-adjusted) whose purpose is to reported here the only criterion considered has been mini• expedite traffic through urban intersections. Although many mum aggregate delay to the vehicles, within the obvious such systems have produced good results, others have at safety constraints of limiting the amount of time a vehicle times systematically aggravated rather than alleviated a may be held by a red phase and the minimum time for a specific traffic problem. In many cases, specialized systems green phase, inasmuch as this approach currently appears implement discrete control philosophies which are artifices most promising. However, the criterion of minimum psy• employed to obtain the minimal-delay results and are very chological delay may deserve further consideration as more limited in their ability to adjust to the rapid fluctuations of becomes known on the subject. urban traffic. Although these special purpose systems some• times are referred to as computer-controlled, the term Because urban areas are in general characterized by their "computer" is here reserved for the general purpose digital geometric grid network and associated heavy traffic vol• computer unless otherwise indicated. umes, they contain a high concentration of signalized inter• sections. It is to these intersections that the major portion To obtain a more desirable system having the sensitivity of vehicular delay can be attributed. Without changing the and flexibility to react to the uncertainty and variability of physical characteristics of the network, the efficient opera• traffic flow that may occur within the time intervals of tion of these signals then becomes a major factor in the practical signal phase lengths, it is proposed that a general purpose digital computer directly implement the basic cri• mechanism (Fig. 1) in which the dynamic network of terion of minimum aggregate delay. Another approach in vehicles, pedestrians, weather, etc., is monitored with the the synthesis of such a system is to program the computer limitations imposed by the detectors employed. The com• to emulate discrete traffic control techniques as currently puter performs the calculations on the dynamic and static employed by individual specialized systems (e.g., progres• information and the resultant decisions or signal displays sive, linked volume-density, etc.) With this method, as control the motorists and pedestrians. noted by Casciato and Cass (5), the computer would neces• The advantages and limitations of any such system, in sarily be capable of assigning various control subroutines vehicle-time of delay saved, are difficult to evaluate ana• to different intersections as dictated by traffic flow (sen• lytically. Specifically, it is suggested that the relative merits, sors), time of day (clock), season (calendar), or the de• when compared to less costly alternatives of some other cisions of a human operator. Because it appears that im• system, be evaluated by computer simulation techniques. plementation of the basic criterion is the more general The ultimate test, of course, is in application of the system approach and would yield the more responsive control to the actual city being studied. (smaller reaction time to changes in traffic demands), syn• A detailed treatment of the material summarized in this thesis of such a system is pursued in detail. chapter may be found in Appendices A through H. The The control decisions of any such traffic-responsive sys• equations given in this chapter are, for the most part, iden• tem should result from continual sampling of the traffic tified by the letter of the appendix and the serial number; flow characteristics and with such speed as to gather and thus, Eq. E-79 in the following text is Equation 79 of process the pertinent data, calculate the decision, and Appendix E. actuate the controls in real time. To process the large quantities of data and perform the many calculations with• DEFINITIONS AND NOMENCLATURE in the required time intervals, the system is synthesized employing a high-speed digital computer. Information de• The basic definitions used in the text of this report are scribing the traffic flow and the signals displayed would assembled here for ready reference. Similarly, the various be fed into the computer from strategically located de• symbols used throughout the text are defined where they tectors, whereas information concerning the street network first appear, but are assembled here for the convenience of geometries (lane widths, number of lanes, location of de• the reader. It should be noted, however, that inasmuch as tectors, etc.) would be stored within the computer for sub• most of the text equations and their discussions are sum• sequent retrieval. The presence-type detectors would yield marized from the various appendices, and each appendix such information as to obtain the volume, occupancy, aver• has its own nomenclature listing, the reader is advised to age speed, and average density across the lanes of coverage, consult such listing for any symbols not contained in the in order to convey the state of the network to the com• following. puter. The computer, working in real time through the A precedent subscript (such as q, or A) indicates the in• programmed equations ithplementing the minimum-delay tersection for which the term is applicable; criterion, would compute the optimum signal display at a A following subscript (such as E, W, N, S) indicates the given time for the entire network. leg for which the term is applicable; Hence, the proposed system may be viewed as a servo- ~ = an estimate of (the term to which it is applied);
COMPUTER: PROGRAMMED EQUATIONS STATIC CHARACTERISTICS (STORAGE)
COMMUNICATIONS COKMUNI CATIONS 'NETYfORK NETWORK'
DETECTORS OUTPUT: PRESENCE, SIGNALS VOLUME, DENSITY, ETC.
• VISUAL COMMANDS NETWORK (DYNAMIC) ELECTROMAGNETIC,ACOUSTIC,ETC. SENSING DEVICES Figure 1. Adaptive-control feedback loop. A = designation of an isolated signalized intersection; MATHEMATICAL MODEL ^ [ ] = with respect to intersection A; a — arrival rate, in vehicles per second; The starting point is observation of signalized intersection D = delay caused within the subnetwork; q (Fig. 2), whose departures are assumed to be "free" ^acc = delay attributed to the time necessary for vehicles vehicles; that is, independent of any downstream intersec• stopped in queue to accelerate to free speed once tion in terms of delay accrued. This situation may occur in they are released; practice when the nearest instrumented downstream inter• ^(icc — delay caused by deceleration of vehicles joining section is far enough away to be considered independent. the end of the queue; Further, it is assumed in the current example that only ^norm — time required to traverse unimpeded the distance signals indicating stop (red), go (green), and clearance over which the delay equation applies; (amber) are available for display to diametrically opposed delay experienced by vehicles in queue waiting traffic streams (i.e., north-south or east-west symmetry). to be served by the intersection; Hence, although exclusive pedestrian phases, leading relative delay suffered by traffic held on the non- phases, turning arrow-indicators, etc., are not considered, moving leg; they are logical extensions of the subsequent development. d — departure rate, in vehicles per second; With the proposed control system the digital computer is departure rate, in vehicles per second, from a leg periodically fed information from remote sensors that during the initial portion of the next phase, (j)^, serve to sample the dynamic state of the intersection (i.e., i- a time interval, in seconds; current phase, approach volumes, departure rates, queue }- a second time interval; length, etc.) Based on the minimum delay criterion, the K2 • constants of proportionality; system uses all pertinent information, such as updated de• L-- i^ii +
Figure 2. Events within a At interval during the
displayed at an isolated intersection. The type and choice to the north-south traffic streams, and greater than the of action that may be taken (by changing the signal state) minimum green time, <^oli;,w,„i„- should first be considered. That is, from the assumed sig• nal states there may be only green east-west or green north- Isolated Intersection south, while the opposite legs are red. The clearance The computations performed for an isolated intersection (amber) interval is not considered as an option in the yield the difference between two quantities—the relative strict sense, because it is a required transitory state. How• delay saved by east-west traffic, S^E.^, and the relative ever, the length of the amber interval for any one inter• delay suffered by the traffic being held on the north-south section may be made adjustable as a function of changes in legs, Drixs—as suggested by Miller (4). The two quan• road conditions, weather, and speeds. tities result from an extension of the current east-west Therefore, if the green signal as observed has an elapsed green phase by some increment of time, «A*, as compared phase time greater than the minimum and less than the to immediate termination of the phase. This difference, maximum, the alternative actions that may be considered 6„^t' is defined as are either to terminate the current signal state in favor of the other, or to extend the current phase for a specific and is the objective function which should be made nega• interval of time. If this time interval is denoted by integral tive before a change in signal phase is warranted. units of Af, the control equations must provide for calcu• If the value of 0^, is negative, and if no successive time lation of the relative aggregate delay which would be increments are investigated, it is known* only that the net sufl'ered to the vehicles on all approaches if the signals are changed immediately, or in Af, or in integral multiples of * Although the term "known" is used here, it should be noted that the quantity II is a prediction of what might occur some time in the future and A?. For purposes of developing these equations it is as• as such is subject to the errors inherent in the prediction model. For example, it is not known absolutely how many vehicles will depart or sumed that the current phase is green to the east-west ap• arrive during the next nM seconds, but a good prediction of these values proaches, <^Gii;,W' and the elapsed phase time, <^, 'S may be obtained easily from past and current observations. These predic• tions are denoted m the text by the tilde; for example, d is a predicted less than the maximum red phase, <^,{,x j, . ., as displayed departure rate. delay incurred would be greater by extending the current number of vehicle-seconds required to traverse the distance phase by At than by immediate termination. It is necessary over which the delay equation applies, must be included. to evaluate aggregate delay for proposed extensions of The combined expression for delay for the north and 2At, 36.t, . . ., nAt, to determine if these alternative ac• south legs is tions would yield less delay than changing the signal state ^rlN.S = 0,,,.,.|x.s -t- D,|j;,g -I- D,„.,.ix,g — DnomilN.S (D-9) immediately. Figure 3 expresses the queue length for a particular ap• Isolated Savings Expression proach leg (number of vehicles in queue) as a function of time. In order to evaluate the savings expression, S^K.^. it is Although all vehicles required to stop at an intersection considered as the sum of two separate terms. The first will suffer some delay, when compared to a free-flow con• term, 5^, is a result of the delay saved due to the departing dition, only those (additional) vehicles impeded by the vehicles during the proposed extension, nAt. The second Atq extended duration of the queue are considered in the term, S^, is the resultant savings that accrue to the vehicles relative delay calculations of the D,,ee and D,,<,c terms. If it forming in queue behind those that have been released is assumed that all vehicles have similar deceleration and from the stop-line of the intersection during the proposed acceleration characteristics (5), both the aforementioned extension. (The subsequent formation of the queue is delay terms will be proportional to the number of additional served at an earlier time once the signals have again vehicles which must fall in queue. With constants of pro• changed in their favor.) The relative delay saved for in• portionality of Ki and assumed for D,,pc g and D.,<,c s> tersection q may now be written as follows: respectively.
q'SriK.W = n{^I> + "^VIE.W (D-1 ) (D-14) Expressing So by multiplying the total number of vehicles s = ^1 2 ^ predicted to depart the east and west legs during the pro• posed extension, nAt, by the prediction of the total lost (D-15) time gives D^cv S = ^^^2 2 "'S ^
Next is examined the term D,,, expressing the difference •S;) = •! 2 (ditAti + 5,^vM) - {^iiiK.w + $'A|E,W + hi.w] in vehicle-seconds suffered in the queue for the two alter• (G-40) natives. The queue size, N, in general may be expressed as a continuous function of time NU)- This representation The second term of Eq. D-1 expresses in vehicle-seconds is physically realistic, because vehicles do not jump into the relative delay saved which accrues to those vehicles or out of queue but rather flow (e.g., V2 veh/sec). Hence, served earlier in time as a result of the previous departures. Figure 3 may indeed express the general queue size on an The factor must include computation of the total number approach leg to an intersection for two specific cases of of arrivals on both approach legs during the next phase, the alternatives considered. i[ln,w> P'"s those remaining in queue, and then multiplica• The term D„ may be expressed mathematically as the tion of this sum by the time that these vehicles are closer difference of two integrals; thus, (in time) to service. Hence, I'Af nit N'U)dt- i N{t)dt (D-16) ^ ^ 5,,.; A t / However, in order to apply this equation it is assumed that the departure and arrival rates over an interval. At, are n constant. Therefore, the exact discrete representation of D, is written as
{{P-^')''-}''%^- (G-42.G-43) _ At..-] ) d,)At,.-{a,.-dy)-^- Aty\ in which the various a, and terms are defined by Figure 2.
Isolated Delay Expression -2{ + E- ) - («j - ) ^2' (D-18) The delay, D^i^.a, caused to the vehicles on the north and south legs, respectively, by deferring the start of the <^GIN,S The previously mentioned equations, particularly Eq. 1, phase for a period of n\t may be represented by three may be implemented in real time if the traffic quantities of separate delay terms. They are, D,,,.^., caused by the de• predicted arrivals, departures, phase lengths, and measured celeration of vehicles to join the end of the queue, £>„, queue length, etc., are obtained within such time as to experienced in the queue waiting to be served by the inter• permit computation of a decision within At seconds. section, and D.„.,., attributed to the time necessary for those vehicles stopped in queue to accelerate to free speed once Network Considerations released. However, because the term delay was taken to mean the additional travel time above that normally in• The isolated equations for 0„ are applicable in all cases curred, another factor, D,„„.„„ representing the average where the delay suffered at the next signalized intersection N'(t) = QUEUE LENGTH ON THE NORTH OR SOUTH LEG IF THE START OF •fr/M^IS DEFERRED BY TtAt
N(t) = QUEUE LENGTH ON THE NORTH OR SOUTH LEG IF<>^/^5lS NOT DEFERRED I A'At
Figure 3. Queue length vs time.
encountered enroute by the vehicles released from q may point; but at what time they will arrive has associated with be neglected in considering the state of q. Although this is it a very large uncertainty. In such instances it is appar• used as the definition of an isolated intersection, it should ently futile to link the intersection being evaluated with be noted that arrivals to intersection q may be dependent the neighboring ones by estimating the delay incurred at on a neighboring upstream signalized intersection (see the signalized intersection downstream from the released Fig. 4). In this case the predictions of the arrivals to q vehicles. However, in urban areas, and in particular within will reflect such influences. the central business districts, such isolated intersections are The choice to neglect a certain portion of the surround• rarely found. This is attributed to the geometry of the ing network with respect to the decision to be made at in• grid network and to the vehicular and pedestrian volumes tersection q (Fig. 4) is the result of practical considerations attracted to the area, necessitating a high density of signal• and, as was shown, does not imply that such an intersec• ized intersections, and the more or less ordered flow of tion is literally isolated. (The intersection may be influenced traffic which is prescribed by the enforcement of various by conditions at other intersections and in turn, may itself traffic ordinances. influence conditions at surrounding intersections.) It does, A question which logically arises at this point is: "How however, indicate that the intersection is being treated as many signalized intersections downstream from the vehicles isolated because departing vehicles may have to travel rela• released from the intersection being evaluated should be tively large distances before reaching another signalized considered in the network delay equation?" In the most intersection or measurement station, or must pass through general case of an intersection of two two-way streets each a number of unsignalized intersections before reaching the vehicle has the choice of three paths (straight through, left, next signalized intersection. "Isolation" may be caused by or right turns). As the number of intersections being con• travel over a relatively short distance where there may be sidered is increased, the probability of the released vehi• a significant amount of friction, such as sources and/or cles reaching the farthest intersection downstream (in the sinks, or any combination of various degrees of the afore• original direction of travel) is decreased as a function of mentioned conditions. It should be noted that in all these the distributions of the turning movements at each inter• instances it may be possible to predict with a high degree section. Further, one may examine the situation whereby of certainty that the vehicles will arrive at a particular turning movements are prohibited and the arrivals at a
NEGLECTED NETWORK IN J L MAKING A DECISION WITH ®- RESPECT TO SIGNAL 0 SOURCE OF ARRIVALS'/I I" TO WEST LEG OF ®
Figure 4. Intersection of two one-way streets. the equations are extended by considering the delays in• curred in the subnetwork contained within the dashed lines. It is assumed that the signal at q is green to east and westbound traffic, phase ,<^GIE,W It must be decided whether the current phase should be extended by n^t or r-l-l-, ' I terminated immediately. To evaluate the alternatives, the delay accrued by the vehicles up to the time that they depart from the subnetwork (at the perimeter of the dashed en• closure) must be considered. The implementation may take the form of evaluating either the difference in times of service at the perimeter (exit of subnetwork) or the sum of delays incurred at each intersection along the route. The latter approach is pursued here. Hence, the total relative delay or savings is considered to be the sum of contributions from, at most, two signalized intersections Figure 5. Subnetwork (q, r, s, t, u) of signalized intersections. for any particular vehicle. Therefore, the 6„At term for the isolated intersection will be applicable to the total develop• ment and will be the starting point.
Savings fVithin Subnetwork
point downstream are certain but are dispersed only by the The SriK.w term is only part of the total savings within the variance on the mean velocity which has associated with subnetwork, as this is the savings of delay at intersection q it the variance of the arrival times, accounting for the dis• only. The additional relative savings within the entire sub• tance traveled. With the inclusion of one signal, or even network will be expressed as the sum of the individual one stop sign, controlling another intersection between the savings at each of the neighboring signalized intersections, intersection being evaluated and the one downstream, the as follows: standard deviation of the predicted arrival times may be nM^S' = "A* („^ 5 + 5 + ,^, S + „,„ S) (E-1) greater than the duration of the green phase (for the down• It should be noted that the pre-subscript q refers to the stream signal), thus introducing a significant error in the situation whereby the savings equation compares the rela• predicted delay. tive benefits of the alternative decisions to be made at For practical reasons, such as those previously described, intersection q. The double pre-subscript refers to the in• network equations are generally limited to the immediate tersection within the subnetwork where the saving occurs. neighboring signalized intersections, normally consisting of Further, the „5' term does not express the total relative four pairs of intersections, each including the intersection savings* within the subnetwork q, r, s, t, u. This term is being evaluated. denoted by
Subnetwork Problem Statement «^5 = "^'(,5' + ..5riE.w) (E-2) where the last term is defined by Eq. D-1. Each of the This section develops a set of general equations that will contributions to "^^^S is now expressed in terms of the measure the relative delay to vehicles, currently being con• difference in delays suffered at the neighboring intersections trolled at intersection q (Fig. 5), that includes the predicted which would occur if the vehicles are released as a result delay when these vehicles reach the downstream intersec• of the extension of the current green phase at q, or after tions, r, s, t, and u, for the control alternatives assumed being held for the duration of the next red phase, ,I^R|B,W- to be available at q. Although the minimum-delay solu• Therefore, tion is sought in terms of the five intersections of two two- way streets, it is realized that many other network con• "^%.r5 = .,.^'?K,K,,v-„,,Do] (E-3) figurations are possible. However, the most common ones will simply be a modification of the subnetwork shown. where ,.D'^^l^:.« is the delay predicted to be incurred at r, Peculiarities to the sample city are discussed later. to the vehicles released from intersection q after waiting The problem is to decide when is the optimum time to for the next red phase, ,|<^U|K,W. and choosing their path change the signal at q, assuming a symmetrical signal dis• through r; and ^^D" is the delay predicted to be incurred play, where "optimum" signifies the minimum aggregate at r, to the same vehicles that are released during the cur• delay accrued within the subnetwork to those vehicles being rent proposed extension and also desire service at r. The controlled at intersection q. pre-superscript nAt indicates that the evaluation is per• The current conditions at q and the state of the rest of formed for a particular value of n. Similar equations may the network (phase, phase time elapsed, queue lengths, be written for the relative saving at s, t, and u. approach rates, departure rates, various predictions based • This value may be either positive or negative. If it is negative, then on past measurements, etc.) are used to implement the more delay is predicted to be incurred by the vehicles from the east-west legs of q at the neighboring intersections r, s, t. u, if released during the minimum-delay criterion. The isolated case was concerned proposed extension, nM, than if held at q for the subsequent red phase, iil^HiK «• ^"^ released. The term "savings" is always applied to the solely with the delay associated with intersection q. Here, vehicles on the legs currently receiving the green signal. Delay Within Subnetwork (5) A. = A. 4- S' — D' (E-79)
Up to this point the "savings" of delay, ^S, within the subnetwork for those same vehicles predicted to receive service at intersection q (east-west legs), during the alter• q©«At = "^^ { (q5 -J)) + {rS-rD)+... („S - „£>) ) natives available at q(0,^K|E,^v). have been considered by (E-80) comparing the delay experienced downstream at the neigh• The computer will perform the following test: boring intersections. If The expression for the relative delay*, J), caused within (E-81) the subnetwork is defined in terms of the previously q0At^O defined delay at q, Z)r|N,s, and the relative delay accrued to extend the current phase, because more or equal delay is the vehicles at the neighboring intersections which are predicted to be accrued by terminating the current phase. predicted to be released from the north and south legs of q. However, if Again, the predicted consequences of the two alternative (E-82) actions at intersection q—(1) Terminate current phase, q0A^ < 0 initiate q<^Glx,s "ow, or (2) Defer action by the extension less delay would be incurred by changing the phase now of q<^GlE,w through nA*—are compared. First, the delay than \t from now. However, it may be necessary to calcu• caused within the subnetwork is expressed as late „©2i„ (,®;,Af, • • -.qOnAt. because less delay may be in• curred at these other times. It should be noted that if any (E-44) of the subsequent ,,(H)'S are positive the procedure may where terminate and the particular extension whose 0 yields a positive quantity is accepted. nMjy = «A*(^^ + + ^j) + ^^j)) (E.46) A descriptive flow diagram of the calculations to be From a previous definition, the first pre-subscript indicates performed at each intersection once every A' seconds is the intersection to which the decision is applied and the shown in Figure 6; its mathematical equivalent, in Figure 7. second indicates the particular intersection at which the relative delay is considered. MEASURED TRAFFIC QUANTITIES Now, a particular intersection, r, within the subnetwork To implement the developed minimum-delay equations, q, r, s, t, u, is investigated. By referring to Eq. E-10, the the computer must "know" both static information and the relative delay at r may be expressed as value of the current dynamic traffic parameters. The static ,.,D=,,,(D«A'-Z)*AiK,w)s,:,,s (E-47) information is relatively fixed and may be entered into the computer and updated infrequently (weekly, monthly, an• where nually). It represents physical quantities that need not, q,i£>siN,s"'^* = delay suffered on south leg of r, to those or in some cases cannot, be included in the real-time feed• vehicles released from the north-south back loop. Included in the table of static information would legs of intersection q, if the current phase be the number and definition of the intersections contained q
* Although this term is denoted as "relative delay," it should be noted does not actuate any of the signals directly (Fig. 8). In• that its sign may be positive or negative. If it is negative, vehicle-seconds stead, all information is fed to the computer, which in are predicted to be saved within the subnetwork by the north-south depar• tures if deferred an additional nit seconds. turn performs the calculations necessary to evaluate the 10
START
MAY THE SIGNAL STATE BE CHANGED? (IS THE ELAPSED GREEN TIME GREATER THAN THE MINIMUM, AND THE RED TIME, AS VIEWED BY THE WAITING VEHICLES, LESS THAN THE MAXIMUM?)
T T
FROM THE CURRENT AND PAST MEASUREMENTS; PREDICT DEPARTURE RATES, ARRIVAL RATES, Z'. HOLD CURRENT SIGNAL-STATE PHASE LENGTHS TURNING MOVEMENTS, ETC., PERTINENT TO THE CALCULATION OF THE DELAY WITHIN THE SUBNETWORK, TO THE I VEHICLES CURRENTLY AT THE INTERSECTION 3. GO TO NEXT SIGNAL IN NETWORK q> AND REPEAT FROM "START"
3. CALCULATE THE PREDICTED DELAY TO THE VEHICLES WHICH WOULD BE RELEASED FROM INTERSECTION q DURING THE PROPOSED EXTENSION, AND FOR THE ALTERNATIVE OF NO EXTENSION.
CALCULATE THE PREDICTED DELAY TO THE VEHICLES WHICH WOULD BE RELEASED FROM THE OPPOSITE PAIR OF LEGS AFTER THE PROPOSED EXTENSION, AND FOR THE ALTER• NATIVE OF NO EXTENSION.
5. COMPARE THE ALTERNATIVES IN TERMS OF VEHICLE-SECONDS SAVED AND MAXIMIZE THE FUNCTION.
6. DETERMINE ACTION AND IMPLEMENT: EITHER 1) CHANGE SIGNAL-STATE OR 2) HOLD SIGNAL-STATE.
7. GO TO NEXT SIGNAL IN NETWORK AND REPEAT FROM "START".
Figure 6. Descriptive flow chart of the implemented criterion.
entire network. Information concerning the current signal be selected for various portions of the day to anticipate display also is included. Calculations are performed to any regular fluctuations. obtain the current queue lengths and elapsed phase time For example, predictable fluctuations may include the every At seconds. Velocity calculations also may be in• onset of rush-hour periods, sporting events, holiday shop• cluded with the same basic detector information, if desired. ping, parades, etc., information which may be entered into the computer at the central site. This does not prescribe a PREDICTIONS particular progression, or offsets, splits, etc., but allows the system to remain in an adaptive control mode. However, Predictions of the necessary quantities (future departure the prediction techniques are thereby altered to be more and arrival rates, cycle and phase lengths, etc.) are up• sensitive to the forthcoming situation, which is assumed to dated as a result of each new measurement. Models may be known a priori. 11
DETERMINE CURRENT STATE OF INTERSECTION WHICH WE ARE EVALUATING
PROCEED TO NEXT INTERSECTION W/OUT CHANGE
MIM CHANGE SIGNAL PHASE IMMEDIATELY AND PROCEED TO SUBNETWORK \ ® NEXT MATRIX FOR INTERSECTION GIVEN INTERSECTION /"COMPUTE\
COMPUTE N
EXTEND CURRENT ^ 0 SIGNAL STATE BY lAt GO TO NEXT INTERSECTION {'C tt < > ®
COMPARE @ SELECT LEAST NEGATIVE I CHANGE SIGNAL STATE AT
Figure 7. General flow chart of saving and delay equation criterion.
These predictions and the models employed determine vanced traffic signal system known to be operational is its the sensitivity of the network's signal response to the fluc• reliance on certain expected values. These averages, which tuating traflic demands. Hence, the merit of the proposed are used as predictions of important traffic quantities, may (implemented) control system obviously relies on judicious have the added flexibility of being varied as a function of selection of the prediction techniques. time (clock), season (calendar), observations (human), One of the problems that plagues even the most ad• etc. However, these predictions are generally based solely 12
COMPUTER SYSTEM FIXED *ND VARIABLE OAT* STORAGE; COMPUTATIONS PHYSICAL OESCRIPTORS OF STREET-NETWORK I CURRENT QUEUE LENGTH (NO. OF LANES, STREET LENGTHS) CURRENT ELAPSED-PHASE TIME MINIMUM GREEN-TIME PER INTERSECTION CURRENT DEPARTURE RATES MAXIMUM RED-TIME CURRENT ARRIVAL RATES DETECTOR LOCATIONS <-l— UPDATE PREDICTIONS OF FUTURE CYCLE LENGTHSl DEFINITION OF EVERY SUB-NETWORK UNDER CONTROL ARRIVAL RATES, DEPARTURE RATES, etc, STATISTICAL VALUES (AVERAGE VEHICLE LENGTH etc.) I COMPARISONS OF DELAY FOR EACH ALTERNATIVE DURATION OF AMBER-INTERVAL (WHEN NON-ADJUSTED) I WITHIN THE SUBNETWORK TRAFFIC ORDINANCES (TURNING PROHIBITIONS) CONTROL DECISIONS IMMEDIATE PAST VALUES OF MEASURED AND PREDICTED DECODE INPUT QUANTITIES CODE OUTPUT
_L INPUT: FOUR POSSIBLE STATES PER INTERSECTION; FROM SIGNAL. TWO POSSIBLE STATES PER DETECTOR; INPUT AT IHPUT/OUTPUT^ A RATE OF APPROXIMATE 60 SAMPLES PER DETECTOR. TUNED RECEIVERS, MULTIPLEXORS. OUTPUT; COMMAND, EITHER HOLD OR ACTUATE, AT MOST ONCE PER A t; TO SIGNAL. > 1 CARD READER PRINTER PUNCHER • CENTRAL SITE CITY STREET-NETWORK y TRANSMISSION MEDIA
CONTROLLERS ADAPTED DETECTOR INFORMATION TRANS• TO BE OVERIDDEN BY FORMED INTO A SIGNAL BY COMPUTER AND TO ACCEPT A UNIQUE TONE GENERATOR COMPUTER COMMANDS
LOCAL SIGNALS VEHICLE DETECTORS Figure 8. Integrated control system, both central site and street network.
on past measurements observed during the last hour, day, instrumentation limitations) complex factors. For example, or year. Furthermore, the measurements may have been departure rates at a particular leg of an intersection may be taken at other than the particular intersection or locale to affected by time of day, day of week, season, weather, which they are applied. Such a philosophy might be ac• turning movements, actual delay experienced in the net• ceptable for a freeway or highway where the statistics at work, length of queues, special local events, international various points may be assumed invariant as a function of news, personal and emotional experiences, etc., some of location. Applying this approach to urban traffic predic- which may be correlated with each other. Based on the tands could lead to poor control. foregoing discussion and the traffic data analyzed, it is It is the very nature of the traffic characteristics experi• believed that the proposed system should lend itself to enced within urban areas to include large variations in the updating techniques that include the most recent informa• important quantities necessary for effective real-time con• tion, when necessary. Hence, as the computer continues to trol, which cannot be forecast with outdated observations. interrogate the remote instrumentaton (sample the dynamic These wide fluctuations occur not only from day to day, or network), the predictions would be revised to reflect these hour to hour, but also within seconds. For example at the additional data. In this manner, an attempt will be made to stop line at the north leg of a hypothetical intersection de• make the system respond to both sudden changes in condi• partures have been flowing at the saturation rate since the tions affecting the predictions and the more subtle variations end of the starting transient. Suddenly a vehicle desires to which occur throughout the day. turn left, but must wait for a gap in the conflicting traffic. Although it is not the purpose of the current study to In a matter of seconds the flow could have been reduced empirically validate various prediction models, such a study to zero. One problem suggested by this example is that of would be necessary for the successful implementation of a obtaining a good prediction of the departure flow subse• control system, and should be performed (in part) before quent to the turning movement. Such a prediction would a system is made operational. In view of the foregoing best be made by including all quantities known to be cor• limitation, the authors investigated a few theoretical pre• related with the flow rate and the most recent measurements diction methods that appeared to be reasonable in their attained by the system. It should be noted that not all of applicability to the developed equations, and also relied on the necessary predictions to be made are as critical or as the empirical validation of other research work in this fluctuating as in the example described. area, such as reported by Miller (4) and Greenshields and The variances on the traffic quantities are believed to be Weida (12). attributed to both attainable and unattainable (due to In selecting the prediction models the computational re- 13
quirements of the digital computer were considered, be• 4. Be able to include the most recent observations with• cause the prediction is most valuable if it can be computed out complexity (easily updatable). simply and quickly so as to be applied within the real-time limitations. In view of the foregoing, an exponentially weighted mov• It is believed that good predictions of the necessary ing average is proposed for use in predicting various traffic traffic quantities (those with small possible errors) may quantities. These averages have been widely used for the be obtained by combining simple linear regression, multiple operation of inventory control systems. Exponentially linear regression, and average values, with a weighted weighted moving averages are used to extrapolate a sales moving average technique. The complexity of the particu• time-series (forecast sales), because they can be made lar model proposed for each of the quantities to be quickly, easily, adaptable to electronic computers, with a predicted will depend in part on the apparent physical minimum amount of information, and to introduce current reasonableness of the assumptions, the prediction interval sales information (//). Furthermore, Miller (4) presents required (confidence level), and the instrumentation as some empirical studies that to some degree validate the proposed. application of such averages to the predictions of certain traffic quantities needed for urban signal control. Use of Averages as Predictions In order to update the exponentially weighted moving average to reflect the additional information of the most There are various types of averages, which at first inspec• recent observation, y„, one must simply add to this mea• tion appear to be good for predictions in general. Spe• surement the product of the weight, p, and the difference cifically, it is desired to predict certain traflic quantities between the measurement and its previous prediction, within the urban network that may be implemented by a (Ji — ^o). Figure 9 indicates the time sequence of events digital computer in making real-time control decisions. occurring when the current observation is to be included. With respect to this application, the properties of these This technique also lends itself to simple and multiple averages (and predictions in general) appear to be as linear regression, where current measurements of the pre• presented in the following. The averaging techniques dictor quantities must be included. should: 1. Include as many of the past observations as practical. Proposed Prediction Models 2. Weight the observations to give more importance to The following is a discussion of the manner in which the the more recent rather than to the earlier observations. values of two predicted quantities may be obtained. For 3. Require simple calculations in order to minimize one of these quantities an alternate scheme is shown. computer size and solution time (real-time applicability). The first prediction is that of "lost" time to a particular
t-At t +At
OBSERVATIONS: PREVIOUS CURRENT FUTURE I MEASUREMENT MEASUREMENT MEASUREMENT | (Y.,) I J 4
PREDICTIONS: 'PREDICTION PREDICTION PREDICTION ^OF "PREVIOUS, 'OF "CURRENT OF "FUTURE MEASUREMENT" MEASUREMENT"/ MEASUREMENT ,
CURRENT POSITION + TIME "IN TIME" Figure 9. Updating prediction technique. 14
CITY OF WHITE PIAINS WESTCHESTER COUNTY NEW 4YORK
^5
mm mm
T fr-y^' 'til i^^-n LliJ/ //
LEGEND •REPRESENTATION IS NOT OF • SIGNALIZED INTERSECTION^ THE COMPLETE CITY BUT -^ONE-WAY FLOW DIRECTION J / INCLUDES THE MAJOR AREA. Figure 10. Locations of signalized intersections in White Plains, N.Y 15
set of legs at a specific intersection. This lost time occurs activate only the sensors on the approaches facing a green during the portion of the amber interval in which no traffic signal. flows through the intersection. The value of this lost time, ^'AIIO.W. is predicted by forming the exponential weighted SELECTING A COMPUTER SYSTEM moving average of the measurements of sensor and the current signal state at the must be calculated from a number of direct measurements. intersection. Also included is the intersection's identifica• Because the duration of the amber phase, 's tion number to assure that the information is used correctly. known, the calculation of the past <^'A,B,W values should be The input data format is shown in Figure 11. performed as the difference between the total duration of When the computer program decides on the action to the amber phase and that portion of <^A|E,W during which be taken with respect to a particular intersection, an output the stop-line detector measures a non-zero vehicular flow. word consisting of 9 bits will be generated as shown in The second example of arriving at the value of a pre• Figure 12. dicted quantity concerns itself with departure flow rates, d^, from the stop-line of an intersection. Data Acquisition Requirements One method simply uses the exponentially weighted moving average of departure rates, over corresponding in• The input word is presented to the computer at a rate of tervals. These are referenced from the start of the green 60 samples per second, whereas the output word is gen• phase, <^oiE. and are taken over consecutive cycles. This erated, at most, once per At for each intersection. To prediction technique for obtaining d^. has the advantage of determine if a new vehicle is approaching the intersection, being both simple and yielding values which apply for a a "01" combination is needed from the approach detectors, full cycle in the future. However, it is believed that better indicating that at the time of the previous reading there predictions of rf„; may be necessary in certain applications was no vehicle (0), and at the current reading a vehicle to the equations. is sensed (1). Hence, a multiple linear regression, which linearly re• In the case of the departure detectors a combination of lates both the number of vehicles in queue and the mea• bits yielding "10" would indicate that a vehicle has de• sured departure rate during the previous interval, A^, to the parted from the stop line. When the approaching or de• prediction of the departure rate during the subsequent in• parting vehicle is sensed by a detector, an appropriate tervals, is proposed. storage location is updated by the computer. This tech• It is believed that the general form of the prediction nique yields a current vehicle count to be employed in the model would be necessary at intersections where left turns programmed calculations. are permitted, with the associated conflicts. A decoding scheme, to be implemented by the computer, has been devised. It is proposed that each possible com• bination of the detector information be stored in the com• APPLICATION TO A CITY puter. From the eight bits containing the approach de• Inquiries were sent to a number of cities with populations tector information, 256 possible combinations exist, of of 50,000 to 100,000 within a 500-mile radius of Cornell which 175 indicate at least one vehicle approaching. The Aeronautical Laboratory. A few replies indicated that the responding municipalities had acquired sufficient traffic data to be useful for this study. What was needed was a typical traffic model. Based on the physical character• istics, available data, and reasonable proximity to CAL, I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 White Plains, N. Y., was selected as the sample city. White Plains, New York, is 9.8 sq mi in area, has a pop• ulation slightly in excess of 50,000 and a trade area for "6 shopping of greater than 250,000, and currently has 116 SIGNAL OR OR INTERSECTION NUMBER signalized intersections (Fig. 10). By looking at each CONDITION Dj signalized intersection with respect to its distance from Figure 11. Input data format. the closest signalized intersections, one-way streets, traffic movements, etc., subnetwork categories were determined as given in Table F-3. It should be noted that each of the 116 signalized inter• sections was treated with equal importance; that is, the 4 5 6 7 8 9 minimum-delay equations were applied, without prejudice, to each signal. As a result, it was estimated that 464 vehicle detectors would transmit information to the cen• tral site at any instant. The stop-line sensors were wired INTERSECTION into the local controller so that they time-shared the de• ACTUATE NO. tector electronics. The signal switching mechanism would Figure 12. Output data format. 16 two stop-line detectors use only 4 bits of data, which give approximately 37,000 words of core storage are needed. 16 possible combinations. The total number of calculations in the foregoing analy• The decoding scheme will not require more than 76 sis must be performed within Af seconds. If At is assumed computer cycles per intersection to decode. This number to be 2 sec, the performance of 900,000 cycles within 2 was arrived at by programming, for the available com• sec implies a cycle time of 2.22 /uSec. puting system, the case where a vehicle is detected simul• taneously at each detector. Summary of Combined Requirements Based on calculations for 116 intersections and the 60- samples-per-second scanning rate, the time per computer The analysis results in the following requirements to cycle for data acquisition was found to be 1.89 microsec achieve the projected data rate and computational schemes: per cycle. Associated storage requirements were allocated 1. For the computational scheme, a computer should: as follows: (a) Perform 900,000 cycles in 2 sec (i.e., have a 116 for the previous Dg —Dg detector data computer cycle time of not more than 2.2 ^sec). 116 for the previous Di — D3 detector data (b) Have floating point capabilities (software or 116 for the previous Dj —D4 detector data hardware). 928 for the vehicle counts at each detector (c) Have address modification features (e.g., index 400 for the computer program (approx.) registers or general registers). 335 for contingency and/or expansion (d) Have a minimum of 37,000 words of core stor• 2,011 total for data acquisition age. (e) Have a data channel. (f) Have a real-time clock. Delay Calculation Requirements 2. For the data accumulation scheme, a computer To evaluate the computer size and speed for the compu• should: tations to be performed with respect to the minimum-delay (a) Perform 76 cycles in 143.6781 /isec (i.e., have equations, three basic expressions were defined as follows: a computer cycle time of not more than 1.89 ;usec). Ti = estimated delay saved by those vehicles served (from (b) Contain a minimum of 2,000 words of core the two legs) during \t, which otherwise would have storage (18-bit words). to suffer the amber, red, and lost time resulting from (c) Have address modification features (e.g., index an immediate change in phase; registers or general registers). T2 = delay saved which accrues to those vehicles served (d) Have a high-speed data channel. earlier in time as a result of the previous departures; and Available Computer Systems T3 = additional relative saving within the subnetwork, ex• pressed as the sum of the individual savings at each As a result of matching the specifications that were previ• of the neighboring signalized intersections. ously developed with off-the-shelf (existing) computer equipment, two possible systems were investigated in detail. The expressions T^, T^, J, were programmed in FOR• The first is to acquire a single computer that can perform TRAN IV (9, 70). both sets of requirements sequentially in the specified time By using 10 cycles for a multiplication and 18 cycles limit. The second system uses two computers—one for for a division (S), the total number of required cycles was input-output and data storage, the other processing the computed for each equation, with the following results: data and making control decisions—operating in parallel. Ti — Equation Type 1, 155 cycles Details on cost analyses of the two schemes are given in = Equation Type 2, 565 cycles Tables F-4 and F-5, respectively. Js = Equation Type 3, 822 cycles Both systems rent for about the same amount, $9,700 per month. Outright purchase of System A would cost Since White Plains, N. Y. was used as the typical city, approximately $412,000, and would require a monthly the 116 signalized intersections were categorized into 5 outlay of about $500 for maintenance. The costs for Sys• different types. Table F-3 shows the types of intersections tem B would be about $358,000 and $1,315, respectively. with the proportion of each, and the size of the "saving" Over a 5Vi-year period, both systems would total about and "delay" equation necessary at each type, together with the same expenditure, $445,000, or $6,740 per month. The the required number of computer cycles. The results indi• cost for the programming effort, to get the system into cate that the total computational scheme will require ap• operation, is estimated at $25,000. proximately 900,000 cycles. Also estimated were the storage requirements for the Additional Utilization of Computing System data that will have to be stored during the calculations (measured departures, predicted departures, measured Aside from doing the traffic controlling, either computer arrivals, predicted arrivals, queue lengths, length of the system could be used for the city's business and adminis• signal phases for each intersection). These requirements trative data processing requirements. This can be done totaled approximately 30,000 words of core plus 20 per• during a part of the day when the traffic is light and control cent for contingencies and program instructions. Thus, can be handled satisfactorily by the local signal controllers. 17
APPROACH DETECTOR
VEHICLE DETECTORS N> APPROACH • DETECTOR s
s 4 APPROACH 3 DETECTOR t
I AND 3 OR 2 AND H TRANSMIT DATA DEPENDING UPON CONDITION OF SIGNAL CONTROL PHASE (GATED BY YELLOW AND GREEN)
APPROACH DETECTOR Figure 13. Intersection configuration.
In addition, the computer may be employed as a tool in has been designed. The instrumentation for the detection the post-analysis of traffic data, as collected throughout the of the state of the signal, together with a phase pattern and control periods or at other specified times, in order to im• coding table, is shown in Figure 14. Only conditions of prove its control function. It may also be used in the per• three bulb circuits (red and green circuits along one line formance of accident studies, etc. of travel, and green circuit for the crossing line) are needed for determination of signal state. INSTRUMENTATION Input Logic Figure 13 shows an intersection with eight vehicle detectors —four located at the stop lines and four several hundred The data from each intersection must be transmitted to a feet upstream on the approach lanes. This represents the control site where the computer is housed. Because all maximum amount of detection equipment required at a information is of an on-off (binary) nature, a selective single intersection. The sensors proposed are of the induc• signaling system using telephone lines could serve as a tion loop type, which initiates detector contact closure when transmission medium. Each channel of information would a vehicle passes over the loop. To minimize the amount of have an assigned signal frequency. At the central site tuned detector electronics necessary, a time-sharing technique receivers would be used to detect the information. Each would be employed whereby the two detectors for the telephone line would then carry a composite of tone signals stop line would be switched between the four stop-line in both directions, between intersections and the central loops, depending on the phase of the signal. The approach (computer) site. The data from each intersection would detectors would remain active at all times, thereby pro• be decoded and grouped to form a computer word whose viding continuous data on approaching traffic. The logic structure is defined in Figure 11. Data from each instru• circuitry necessary to accomplish the switching function mented intersection are brought to the central site con- 18
"NS piled for the complete installation. The breakdown was as follows: Intersection equipment, @ $1,575 $182,700 ASSUMING THAT NO SIMULTANEOUS T.6. Input logic interface at central site 26,530 "NS'^EW CONDITION OCCURS Output logic interface at central site 19,740 "EW Telephone line leasing 2,000/mo. MIXED T.G. OUTPUT Total $228,970 plus
°NS $ 2,000/mo.
•H T.G. T.G. = TONE GENERATOR These figures are approximate, as telephone leasing rates will depend on the community selected. Not included are the maintenance and construction costs associated with the BINARY CODE OCTAL EQUIVALENT OF equipment's installation and upkeep. BINARY CODE "NS 6,N S 6 E_W
I 0 I 5 CONCLUDING REMARKS I 0 0 I
0 I 0 2 There is little doubt that a traffic control system such as the one described in this report can lead to improved traffic movement in an urban complex, when compared to a system that is not traffic responsive. Investigations (J, 4) SIGNAL CONTROLLER PHASE PATTERN have shown that this improvement is purchased at a lower cost than the penalty paid for doing without it. EW
G There are, however, signal control systems that are re• Y sponsive to the demands of traffic, to a greater or lesser CYCLE R degree, that do not use a general purpose computer for R G deciding on signal settings. These systems operate on Y preprogrammed control modes that are called into effect R by measurements at a point, or several points. The great R majority of the controllers use a special purpose analog Figure 14. Monitor for phase condition of signal controller. computer to discriminate among levels of traffic demands in order to call for changes of modes. Flexibility of adapt• ing the control mode to suit the traffic situation is limited by the finite number of modes that are physically wired into the controller. In most cases the cost of these control systems is more than offset by the value of the reduction in tinuously, whereas the computer control commands are motorists' aggregate travel time. sent back to each intersection only as required. Figure The latest entry into the field of traffic control is the 15 is a logic diagram of the input circuitry. high-speed general purpose digital computing machine. A control system using this machine also is preprogrammed. Output Logic Unlike the special purpose computer, however, its flexi• bility to meet changing traffic requirements is not estab• The output control signals from the computer are generated lished at the factory, although the storage capacity and at a maximum rate of one every Af seconds for each inter• computing speed, which are determined by the combination section. They consist of a HOLD and an ACTUATE com• of hardware and software components are, of course, limit• mand. When it is desired to transfer a signal at a particular ing physical factors of the machine. Conceptually, the intersection from fixed-time operation (local controller) to control doctrines that may be programmed into the com• computer control the output word presented by the com• puter are limited only by the ingenuity of the analyst who puter will contain a binary "1" in the HOLD bit and the develops the controlling equations and modes. As current corresponding 7-bit intersection identification. Once this and future hypotheses are tested and become candidates has been accomplished, if it is desired to change the signal for practical control applications, the computer generally state the ACTUATE bit must be transmitted as a binary will be unlimited in its adaptability to implement these "1". Figure 16 shows a logic diagram of the output cir• control doctrines. Moreover, these changes are effected cuitry. without adjustments or alterations to the hardware in the field, but simply within the software (the written program SYSTEM INSTRUMENTATION COST and the data input) at the computer site. As one traffic engineer stated the case: "The general purpose computer An investigation was made with reference to the sources of gives me an easy way to correct the mistakes I am going supply for the instrumentation required at each intersection to make, because I don't think I know everything that the and at the central site. Based on the mode of operation traffic is going to do in my city." desired, a typical set of equipment cost figures was com• The justification for considering any traffic control sys- •wvj8vip DiSoj jojtuoo indino atis jojiuso uainduioj -9/ ajtiStj
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OK 009 20 tem must rely on at least two basic premises. First, there is question of what a digital-computer-controlled system a current or future need for improvement; and second, the may accomplish now is being evaluated by researchers at system appears to offer a practical solution when consider• Toronto, Canada; San Jose, Calif.; and Glasgow, Scotland. ing the alternative courses of action. Although improve• The future is more difficult to analyze. It is for this very ments in traffic flow can be achieved by increasingly effi• reason that the digital computer deserves still further con• cient assignment of right-of-way, the level of service must sideration. approach, as an asymptote, conditions at saturated flow. Finally, it is in order to comment on the "minimum- When the demands continue beyond this point, either the delay" control mode that has been developed in this re• service must deteriorate or the inexorable alternative of search. Of the three digital computer systems currently "laying more concrete" must be followed. being evaluated, only the Glasgow program has definite The original problem reduces to that of determining the plans to include a control mode that uses minimum delay increment of service that may be obtained now and in the as a criterion. The others are testing modes that derive future by such an installation. Proverbially, this may be principally from the more conventional schemes of the stated: "How much can my investment buy for me?" The past.
REFERENCES
1. WEINBERG, M. I., "Traffic Surveillance and Means of with Applications to Highway Traffic Analyses." The Communicating with Drivers — Interim Report." Eno Foundation for Highway Traffic Control (1952). NCHRP Report 9 (1964). 13. WOLD, H. O. A., "Unbiased Predictors." Fourth 2. WEINBERG, M. I., ET AL., "Surveillance Methods and Berkeley Symposium on Mathematical Statistics and Ways and Means of Communicating with Drivers." Probability, Vol. 1, pp. 719-761 (1960). NCHRP Report 28 (1966). 14. ROSENBLATT, M. (Editor), Time Series Analysis. 3. CASCIATO, L., and CASS, S., "Pilot Study of the Auto• Wiley (1963). matic Control of Traffic Signals by a General Purpose 15. MOOD, A., Introduction to the Theory of Statistics. Electronic Computer." HRB Bull. 338, pp. 28-39 McGraw-Hill (1950). (1962). 16. ARLEV, N., and BUCK, K., Introduction to the Theory 4. MILLER, A. J., "A Computer Control System for of Probability and Statistics. Wiley (1950). Traffic Networks." Proc. Second Internal. Symposium 17. KELL, J. H., "Intersection Delay Obtained by Simu• on Theory of Traffic Flow, London (1963). lating Traffic on a Computer." Inst, of Transporta• 5. GREENSHIELDS, B. D., ET AL., "Traffic Performance at tion and Traffic Eng., Univ. of California, Berkeley. Urban Street Intersections." Tech. Rep. No. 1, Yale 18. City of Buffalo, N. Y., "Specifications for Master Bureau of Highway Traffic (1947). Computing Equipment for Two Interconnected Traffic 6. BLUMENTHAL, R. C, and HORN, J. W., "Pressurized Control Systems on Main Street (North System and Intersections." HRB Bull. 167, pp. 42-62 (1957). South System)." 7. KELL, J. H. "Results of Computer Simulation Studies 19. Vehicle Traffic Control Systems, General Railway as Related to Traffic Signal Operation." Proc. 33rd Signal Co., Rochester, N. Y., "Traffic Control and Ann. Meeting, Inst, of Traffic Engineers (1963). Surveillance Computer—Main Street Traffic Control 8. "IBM 7040/7044 Principles of Operation." Form System, Buffalo, New York." A22-6649-4, IBM Systems Ref. Lib. (May 1964). 20. MATSON, T. M., SMITH, W. S., and HURD, F. W., 9. "FORTRAN II General Information Manual." Form Traffic Engineering. McGraw-Hill (1955). F28-8074-3, IBM Systems Ref. Lib. (Dec. 1963). 21. "Research on Traffic." British Road Research Labo• 10. "IBM 7040/7044 Operating System (16/32K) FOR• ratory, HMSO (1965). TRAN IV Language." Form C28-6329-2, IBM Sys• 22. HORTON, T. R. (Editor), Traffic Control, Theory and tems Ref. Lib. (1964). In. APPENDIX A VEHICLE DETECTORS AND THEIR LOCATIONS FOR SURVEILLANCE OF TRAFFIC IN A STREET NETWORK The traffic signal system under study is to be activated by detectors falls off at low speeds, beginning at about 20 mph commands from a high-speed digital computer operating and continuing down to the lowest speed at which they in real time. Surveillance over the movement of traffic, in seem to operate, about 4 mph. The cost of these detectors response to the control system, is to be supplied by vehicle is similar to that of the overhead presence detector. detectors located so as to provide the data required by the The in-pavement magnetic loop detector senses the pres• control doctrine. The following is a discussion of the types ence of a vehicle by the shift of phase in an alternating- of detectors that are appropriate for this purpose, the ways current circuit in which the inductance of the loop and a in which the sensor outputs may be processed, and the capacitance are tuned to oscillate at a reference frequency. number and locations of sensors compared to the informa• The phase shift causes a voltage pulse that is used to acti• tion they might furnish. vate a switch, which can remain closed until the vehicle leaves the loop and the circuit retunes. Because the phase SENSOR TYPES shift is affected by the mass of the vehicle and its prox• imity to the loop field, there can be significant variations Synthesis of this digital-computer-controlled system has between the leading edge of the vehicle when it first enters been restricted to the use of "off-the-shelf" (currently the loop and its location when the loop has recorded available) equipment so that the descriptions of the de• a detection. Similarly, this variation can exist when the tectors are of commercially available items. Later there vehicle leaves the loop. is a treatment of the manner in which the output from As a result, the time required for a vehicle to pass over one of the sensors might be processed in order to increase the detector loop may be measured with a significant error, the amount of information, over that presently provided, some of which may be biased out by correlation of detec• that can be furnished to the computer. The detectors are tor output and observation of speed and vehicle length by of the following types: very precise methods, as can be done in the case of over• 1. Overhead pulse-type presence detector. head presence detectors. Prices for loop detectors vary 2. Overhead continuous wave (CW) Doppler velocity from $120 to more than $500. detector. Each of the detectors described will furnish a digital 3. In-pavement magnetic loop presence detector. count of each vehicle that activates it. The overhead pulse-type presence detector is used ex• tensively in traffic signal control and, to a lesser degree, for SENSOR DATA PROCESSING the acquisition of data on traffic flow. It uses time-lapse discrimination to distinguish between return of a pulsed The sensors used in the vehicle detector systems provide super-audio acoustic signal from either the pavement below raw data that could be processed in ways different than they the detector or a vehicle over the echo "spot." Because of are. For instance, the overhead presence detector uses a time required for the pulse to traverse the usual 36 ft from logic circuit that closes a switch when, after a period of transmitting to receiving transducers (18 ft above the pave• time that spans two pulses, the echo time for the pulse is ment) in cold weather, the pulse repetition frequency (prf) shorter than some selected value. Thus, when two suc• is limited to about 25 cycles per second. This discrete cessive pulses indicate "vehicle" presence it is assumed that limitation determines the accuracy with which the time can a vehicle is present with negligibly low probability of be resolved that a moving vehicle spends under the detector, "false alarm" (spurious signal). Similarly, the switch is a point that is discussed in some detail in NCHRP Report opened when this same logic is satisfied for the "no vehicle" No. 28 (2). Vehicle speed is estimated by dividing a indication. Another version of this detector, using the same previously statistically derived average length of vehicle by sensor and costing about 50 percent more, is able to dis• the time spent under the detector. The latter quantity is criminate the time delay for the echo at a second level, thus computed as the number of "vehicle presence" returns di• providing ternary information. It classifies vehicles as vided by the prf. These detectors are fairly reliable and "high" or "low," as well as determining that there is no cost something over $500 each plus the cost of a supporting vehicle. structure for the sensory device. It is evident that the time delays could be measured on The CW Doppler velocity detectors use both acoustic an analog basis, if so desired. The result would be a set and radio frequencies for signal radiation. Both types of echos that would establish the "profile" of the vehicle measure Doppler frequency shift to indicate the velocity of that passed under the detector, the resolution of the profile an approaching vehicle. The bandwidth of the frequency being dependent on the vehicle speed, for a given prf. filters determines the resolution of the speed indications. Such a profile might be used to identify the type of vehicle Pra< tical applications have shown that the accuracy of the much more closely than is afforded by the "high" or "low" 22 classification. The technique that might be used to match or one vehicle waiting for passage. Also, there can be no the acquired profile with some known profile is not dis• assurance that counts from upstream can be used to foretell cussed here other than to comment that it could be done by queue length unless turns are prohibited. The condition is any of several signature recognition methods (map match• too restrictive, making a detector location at the stop line ing, Fourier analysis, etc.) relatively poor. As shown in Figure A-1, movements at The CW Doppler sensors used as velocity pick-ups trans• intersection 2 will not reveal the number of vehicles moving mit and receive "tones." Unless their designs were to be toward intersection 1, except on a statistical basis, because changed quite radically, they are limited pretty much to turns and through movements at intersection 2 cannot be their present performance. For instance, if the antenna resolved. were to operate as a "seeker," as in the case of homing Therefore, if it is decided that the detector must be up• radars, it would be possible to determine vehicle speeds stream of the stop line, the question is, "How far?" A quite accurately from the rate of rotation of the antenna fairly obvious question to be resolved is the length (num• at some specified angle. ber of vehicles) of a queue waiting for a green signal. If The phase shift or voltage change sensed by an in-pave- it is desired to estimate the number of vehicles in the queue ment loop detector is a continuous function that can be that will begin to form when the signal turns red, "how far" recorded as a profile or "signature." These raw data can can be expressed in stopped vehicle lengths (about 23.5 ft be more informative than those acquired from the discrete for passenger cars). Intuitively, it would seem that the prf of the overhead detector, because, in theory, the com• higher the volume handled by the intersection, the longer pleteness of the signature is not affected by vehicle speed. should the signals be phased, implying longer queues (for If a statistical investigation of these signatures indicated isolated intersections) and, therefore, a large distance from that a high level of confidence could be placed in using the intersection to the detector. them to classify vehicles, they could be used to increase Lane volumes for city streets in which intersections are greatly the amount of information going into the computer controlled and time-shared appear to reach 1,100 vph of storage. Not only would the types of vehicles be known, green time (6, Fig. 11). In his mathematical study of the but better estimates of individual vehicle speeds also could effect of variation of cycle lengths and splits in a fixed- be computed because their lengths could be determined time controller, Kell (7) commented that cycle lengths of more accurately. Again, any of the usual techniques for 30 sec were about as short as could be tolerated for lane pattern recognition could be employed. A really powerful volumes of 500 vph. Optimum cycle length for equal vol• discrimination logic might make it possible to separate and umes of 500 vph on each approach, with no turns per• identify two signatures simultaneously sensed by a loop mitted, was 50 sec. "Optimum" means that average delay covering two traffic lanes. for each vehicle was minimum, at 17 sec. Disregarding For the time being, the advantages to be gained by addi• the short amber phase, either 7 or 8 vehicles would pass tional processing of the sensor outputs are considered only through the intersection during the 25-sec green phase. for their academic interest. The control system that will be If 8 vehicles are waiting in queue for the signal, the designed will use only the current output of the instrumen• detector would have to be not less than 8 X 23.5 = 188 ft tation, which is merely binary information on a switch from the stop line to have counted these vehicles. (To position, not the signature profile suggested in the fore• make this count the surveillance system and computer logic going. must be able to identify the lead vehicle of the stopped platoon, a point discussed later.) If the volume is less than DETECTOR LOCATIONS the maximum, and the lead vehicle can be identified, the number of vehicles in the queue can be counted with rea• Two categories of detector installations on each approach sonable accuracy. However, if for some reason the queue leg to an intersection are discussed. In one of these, one exceeds the length to the detector, there can be no knowl• detector location is assumed for each approach leg; in the edge of the location of the upstream end without additional other, two detector locations are assumed. Because of the information from some upstream location. use to which the information on the traffic movements is to An absolute upper limit to the distance of the detector be put and the limitations in accuracy noted for the velocity from the stop line can be estimated from the results of detectors, the employment of presence detectors is assumed. Kell's work. At 700 vph on each approach lane he re• At this time, no comment is offered as to a choice between ported (7) that cycle lengths of less than 150 sec failed, the overhead and loop-type sensors. "failure" being defined as a queue length that exceeded 100 vehicles and average waiting time in excess of 10 cycle One Detector on Each Approach Leg lengths. All cycle lengths failed for volumes above 700 vph. For simplicity, an intersection of two 2-lane streets is used, Assuming the foregoing volume and cycle length, 29 with each street carrying two-way traffic. In this configura• vehicles would have to pass through on each green phase, tion it is possible to have the detector located at the stop giving the longest meaningful queues that might be imag• line or some arbitrary distance upstream. What might ined for an operational system. The length required to happen in each of these cases is considered. store 29 vehicles is 685 ft. This distance is unrealistic; it is If the detector is at the stop line, the only information unlikely that a signal would be permitted to remain on a that can be elicited during the red phase is that there is none 2.5-min cycle at an ordinary intersection. Also, a volume 23 1 L! 1 1 _>J 1 1 1 Figure A-1. Detectors at stop line. of 700 vph per lane is academic; real values would be more gram logic that can use frequency of arrivals over the de• like 500 to 550 vph. Therefore, it seems that a reasonable tector as a clue to average speed of the traffic stream. Such location for a detector at a busy intersection would be a relationship could be unambiguous if it is found that the about 200 ft back from the stop line, unless it was ob• movement of traffic on city streets is always below the served that queue formations regularly exceeded this dis• critical speed, v,.rit (2, App. A), on the volume-density tance. Another consideration might be the control logic's curve that describes the traffic flow. Also, it is possible that need for some minimum time interval between a vehicle's the value of K might be affected by whether or not the passing the detector and its expected arrival at the inter• identified lead vehicle really is at the head of a moving section. platoon, in which case its movement would not be im• Summarily, a desirable location for the detector can be peded by previous traffic. This can be determined by ex• determined from observed traffic flows at an intersection. amining the time gap that preceded the vehicle signal that The set-back should be great enough to include the longest is later identified as that of the leader. queues that are normally expected to form. As this distance is increased, however, the probability of identifying the Two Detectors on Each Approach Leg veWcle that will be the lead car in the queue will decrease. Identification of the lead vehicle can be done from a Because a suggestion to use more than one detector on statistical study by observing the average time lag from each approach to an intersection immediately prompts the passage over the detector to start of the amber phase for question, "Why," the discussion must center on what addi• the vehicle that becomes the platoon leader. It should be tional detectors, and how the benefits to be derived com• noted that there is no way to identify the vehicle positively, pare with the additional cost. short of complete surveillance on the approaches. At this It was stated previously that a presence detector at a time it is not economically feasible to provide the instru• stop line would indicate with certainty that there was a mentation required. Figure A-2 pictures the situation just vehicle waiting for passage, and also could count vehicles as the amber phase has begun; the time h t = f„. From passing. But the stop-line detector has no way of supplying long-term observation it has been determined that when information on the length of a queue, which is an important ta — td — the vehicle passing the detector at t,, will go factor in determining a control decision. It does, however, through the signal. The situation in Figure A-2 is: — lend itself to instrumenting a computer logic to decide if tg., > K, so vehicle 2 goes through; /„ — tg.^ < K, so vehicle a vehicle is waiting for an opportunity to turn left. For, if 3 will be at the stop line and there will l5e at least three a vehicle is "holding" at the intersection, as shown by the vehicles in the queue. If vehicle speeds are sensed, the detector, and a steady stream of counts is coming in from value of K can be made speed-dependent. the detector on the opposite approach, it may be surmised Alternatively, a subroutine can be written into the pro• that the holding vehicle is waiting for an acceptable gap t T2 Figure A-2. Mid-block detector. 24 in order to turn left. Any other "hold" signal would not may be possible to get an expected time of arrival by be normal during green time. extrapolating detected speed over the distance separating A persisting presence signal on a stop-line detector could the detectors. However, this would be done at the expense indicate some sort of trouble, if it continued for a pro• of an indication of presence at the mid-block detector. The tracted period in the face of no sign of conflicting traffic. assumption is made that a presence detector cannot be used Although a similar logic can be written for a mid-block to compute speed of a particular vehicle with satisfactory detector location, which should be just as effective during accuracy. periods of high traffic activity, it will involve a certain Most important of all is that dual detectors upstream of amount of additional delay time before deciding that some the stop line are justified only if they enable the control difficulty exists. system to make consistently better estimates of traffic con• A stop-line detector also will lend strength to the logic ditions than will a single detector, and that the savings in described previously for identifying the lead vehicle of a delay time that may result shall more than pay for the platoon stopped at a signal. It is evident that an indication over-all cost of the additional detectors. (This additional ofr a stoppage at the intersection will invalidate the scheme cost is not in the detectors alone, but must include increased described in connection with Figure A-2. On the other capacity within the computer for data storage and com• hand, if the passage of vehicles at the stop-line and mid- putational logic.) block detectors reaches a fairly steady state during the There appears to be no particular virtue to a stop-line- green phase, this is reasonable assurance that the logic will and-far-side installation, as shown in Figure A-3. If the hold. Actually, it is necessary only that an indication of streets are two-lane, it should be possible to get information vehicle departures at a satisfactory frequency be obtained on turning movements, using an appropriate computer or that no further vehicles are attempting to move through logic. For standard city block spacings, the far-side loca• the intersection. tion probably would be too far upstream for the ideal mid- If the stop-line detector indicates a blockage and the block location, particularly where parking is permitted. identification logic is voided, it is still possible to compute A comment is offered about the use of stop-line detectors the number of vehicles in the waiting queue if, during the in cities in which buses operate. It is possible to include red phase, the queue extends to the mid-block detector. the effect of bus stops in the control system if a beacon in The loop must be long enough so that it will not lie within the bus will radiate a special tone. A scheme of this sort the gap normally expected between vehicles in a queue; if could be used to denote when a bus is approaching an there is occupancy to or past a detector, a presence must intersection or is discharging or taking on passengers. The be shown. This latter criterion must hold for the stop-line loop, acting as an antenna, would pick up the transmitted detector as well. The 23.5-ft spacing of vehicles in a queue signal from the bus and carry this information to a filter is based on an average vehicle length of 17.5 ft and an circuit, where the bus "signature" would be recognized average gap of 6 ft. Thus, it may be suggested that a loop and the computer so informed. length of 10 to 12 ft, in the direction of travel, would be Addition of stop-line detectors at a normal intersection fairly certain to detect any stopped vehicles without losing (Fig. A-1) can be done by using four sensors coupled in discrimination between successive vehicles when they are pairs to two detector electronics packages. It is evident in motion. that no traffic should be passing the stop line on the red Once the number of vehicles in a waiting queue has been phase, so information from the sensor on that approach determined, the counts at the stop line can be subtracted should be trivial. Only when the green light is shown is and those at the mid-block detector can be added to keep the movement, or lack of it, of interest to the control sys• a running inventory on the number of applicants for pas• tem. Therefore, an economy in hardware can be effected sage through the intersection. Although errors are certain by providing for automatically switching the sensor to the to creep in, this method may be used over the course of a detector when the green phase is in operation. Because green phase with high confidence. Then, if the queue information on the state of the signal will be sent to the length can be computed by the means discussed previously, the data can be reinitialized. If not, the data can be ex• tended through each signal cycle, with decreasing con• fidence, until reinitialization can take place. Is there any advantage to a detector location somewhere between the stop line and mid-block? It is obvious that it will give a better idea of the lead vehicle of a queue than will the mid-block detector. A problem still will exist, however, in determining the identification of the times at which a vehicle has crossed each detector for the counts from the two detectors to be correlated to give numbers in the queue. This identification should occur without error, if the use of the second detector is to be justified. Identification without error may be hard to achieve in city I traffic, considering the uncertainties due to acceleration noise. If the mid-block detector uses a velocity sensor, it Figure A-3. Stop-line and departure detectors. 25 computer, the data from the sensor can be sent to the detectors can be used directly for vehicle departures, with• address in the computer for the proper approach leg. out having to accept an estimate and the time lag that Although no particular example is cited, it can be seen would result if the data come from mid-block detectors. that a single detector electronics unit can be time-shared by several stop-line sensors for control of a polyphase sig• CONCLUDING REMARKS nal cycle. This is possible so long as the state of the signal The preceding discussion has been concerned with location is being sent to the computer, so that the data can be of detectors at an isolated intersection of 2-lane streets. processed with proper meaning. Many digressions from this type of intersection occur in The traffic data to be derived by the surveillance equip• a real street network. Thus, it is to be expected that the ment will be used to provide for the solution of a mini• numbers of detectors required to serve the system ade• mum-delay equation, which is discussed in a preliminary quately may vary considerably from intersection to inter• manner in Appendix D. Information supplied by stop-line section. APPENDIX B AN ESTIMATE OF TRAFFIC SURVEILLANCE AND SIGNAL STATE DATA FOR A DIGITAL-COMPUTER-CONTROLLED TRAFFIC SIGNAL SYSTEM This appendix describes and discusses some of the infor• The loop detector is able to distinguish between nothing mation that will be transmitted from the traffic signals and in its field and something that produces enough of a change the surveillance equipment. The incoming data will have in the field so that the detector circuitry can sense the to be coded, transmitted, stored or read directly into the voltage change or phase shift. If the "something" produces computer, and then processed by the computer in order to a sufficiently large signal-to-noise ratio of a reasonably arrive at control decisions. consistent value, it is possible to design the detector so that it can discriminate between one or two "somethings," pos• ESTIMATE OF TRAFFIC SURVEILLANCE INPUT DATA sibly more. In general, the alteration of the field by a single vehicle is not a step function of constant value, so that posi• In addition to developing the "software" for the control tive discrimination reduces in probability as the number of system, it is planned to synthesize the hardware elements, lanes covered by the detector increases. In this study it is over and above the actual traffic lights and local signal assumed that no loop will be installed across more than controllers at each intersection. To do this, a number of 2 lanes. decisions must be made concerning the equipment. For On a statistical basis, the loop detectors will be credited instance, the average number and types of traffic sensing with the ability to sense the "length" of the vehicle with detectors must be estimated, assuming that detectors are sufficient accuracy to provide a measure of lane occupancy. installed at each signalized intersection. The number of However, it is possible to set the signal-to-noise threshold data communication and signal control lines needed will level high enough so that leading or trailing portions of depend on the type of sensors used and their information the vehicle will lie within the field and yet a null signal rates, as well as the degree of flexibility designed into the will be registered. This latter point applies particularly in control logic. the case of the multilane application. Here it is possible The City of White Plains, N. Y., was selected as having to mistake one vehicle for two, or vice versa, depending on a well-documented traffic "model," which was used to the discrimination threshold levels and the amount and determine the requirements for the system. The city cur• distribution of electromagnetic material in the vehicles. rently has 116 signalized intersections, some operating in• To illustrate this latter point. Figure B-1 shows the hypo• dependently and others working in groups to provide co• ordinated control. thetical signature of a large tractor-trailer truck and a small imported vehicle. The traces show the voltage levels as It is assumed that there will be an average of 4 detectors at each signalized intersection, or a total of 464. If each the vehicles pass into and out of the zone of sensitivity of detector is used to record vehicle counts on one lane, the the loop. If the two vehicles reached the loop simultane• frequency of interrogating such a detector will be different ously, as shown, there might be a significant time lag before than if it is used for surveillance over more than one lane. the loop output rose to the two-vehicle level. Also indicated (In Appendix A it is suggested that the most suitable type is the possibility that the signal might fall to a low enough of detector for this application is the magnetic loop in• level along the length of the truck so that a small car also stalled in the pavement.) might be within the loop without its presence being known. 26 Two-vehicle threshold Single vehicle threshold Truck Small car Null signal Time Figure B-1. Analog trace from loop detector. Yet if the two-vehicle threshold is set low enough, the in different lanes. For the sake of simplicity, the signatures truck could look like two vehicles to the detector. Actual are shown as "square waves" in Figure B-2. It can be seen performance of the detector system must be based on the that, to determine that the signal is not at constant level vehicle signatures. A decision on the accuracy of the ter• from the front of the first vehicle to the rear of the second, nary-level (2-lane) system must be held in abeyance until the empty space between the two must be resolved. To do the signature traces are available. this, the interrogation frequency must be at least as high as Once the decision is made that the detector circuitry is the reciprocal of the time period for the empty space. Thus, adequate for 3-level discrimination (probably on a statis• the frequency becomes a function of the desired accuracy tical basis) it must be determined what accuracy of count• of counting a distribution of arrivals in which a specified ing can be obtained. It is evident that arrivals of vehicles empty space time period (or less) has a certain probability over the loop can range from simultaneous to tandem. of occurrence. The following example indicates the man• The solution to the counting problem would be simple and ner in which this frequency can be computed. straightforward if the signatures were fairly sharp step Suppose the time headway between vehicles moving at functions and of reasonably uniform value, and if infor• 40 mph is 2 sec. Then, in a uniform distribution of head• mation from only one detector was being used. ways between vehicles in separate lanes there will be 1 But the signatures may not be step functions and many percent of the distribution in each 0.02 sec of headway. detectors will be feeding information to the computer. Therefore, to arrive at a counting accuracy of 99 percent This results in a problem of time-sharing for the detectors, at a confidence level of 1.0, the interrogation frequency for which a frequency must be determined that will pro• would have to be 50 cps or higher. vide adequate resolution for sensing the arrival (and de• Some difficulty that might be experienced with voltage parture) of vehicles. level (or phase shift) discrimination, as shown in Figure The lowest frequency at which any single detector for B-1, might be eliminated if the count is made on the dif• a single lane may be interrogated will be that for the short• ferential of the voltage (or phase change) with time. Cer• est time period that a vehicle will be over the loop. A tainly it would seem reasonable to expect that a vehicle small car, perhaps 100 in. long, traveling at 60 ft/sec (40 entering and leaving a loop of short length compared to mph), will pass a point in 0.139 sec (7.2 cps). At any that of the vehicle would cause a fairly sharp rise in signal, but very low speeds, the length of the vehicle will be less followed by some shallow undulation and then a sharp than the space between vehicles, the latter being about 6 ft drop. If, then, the differentiated voltage rate is plotted, the when a line of traffic is stopped. signature would appear as in Figure B-3. Some minimum When the loop is required to cover two lanes, the inter• value of de/dt is established as a threshold. rogation frequency requirement changes drastically. Sup• The plot of de/dt vs t shows that the leading edge of the pose, as shown in Figure B-3, the signature after processing two signals that were used as signatures would appear to is a voltage level for two vehicles at close proximity but the detector as coming from one vehicle. However, the 27 Vehicle No. 2 Single-vehicle threshold Vehicle No. 1 Null signal Time Figure B-2. Single loop, two traffic lanes. number of times this might occur in a random distribution entered the loop at 40 mph, the time period would be 0.033 I of traffic in two lanes would be very small. Not having sec, calling for an interrogation frequency of 30 cps just any signatures to examine, the time period over which to "see" de/dt. If the computer was to be able to discrimi• de/dt might exceed some arbitrary value cannot be com• nate between successive vehicles at close proximity in ad• puted, although it is certain to be quite short. For instance, jacent lanes, the interrogation frequency should be about if full voltage rise took place as the first 2 ft of a vehicle double this value. Time, t Time, t Figure B-3. Analog trace and time derivative. 28 From the foregoing discussion it is surmised that a 60-cps from information on just one approach, if a simple cycle interrogation rate may serve as an initial value for design and fixed amber phase is used. purposes. Thus, the total amount of information that can Communication of signal condition can be by tone trans• come into the computer during a sampling period will be mission, step voltages, or separate lines. An encoder will the frequency times the sampling period times the number be required at the signal end of the line for tone transmis• of detectors, or 60 X 1 X 464 = 27,840 bits per second. sion and/or a decoder at the computer for either stepped voltage or tone transmission. Decisions on which arrange• DATA LOGGING ment to use would depend on relative cost and reliability. Thus far, each detector will require two words of core The data sampling period is assumed to be 1 sec. This storage, one for occupancy and the other for volume. In time period is considered because it would be close to the addition, an undetermined core capacity will be required frequency of arrivals or departures at saturated flow on a to add occupancy bits into the register and to conduct the typical small city street. It is estimated that such a city logic for adding volume counts into its register. would have main streets on which there would be two A typical fixed-time cycle controller with provisions for active lanes on the approaches and that saturation could manual control can be operated by the computer control approach 1,800 vph. system by two commands. One will be the command to Thus, if the detector interrogation rate is 60 cps, logging convert from fixed-time cycle to manual (energize a holding of time occupancy may require storage of as many as 60 relay; failure reverts to fixed cycle) and the other is the "vehicle presence" indications. This can be accommodated command to change phase (a power pulse long enough to by 6 binary bits. Since practically any digital computer of energize the solenoid that drives the phase change cam). reasonable size will have a core storage of 12 or more bits Three signals (or their absence) will inform the com• per word, 464 words in the core will hold the raw detector puter of the signal state, assuming a simple four-approach inputs. This assumes that the register will store in binary signal light with no special phases. (Such a signal opera• form. tion is discussed more fully in a succeeding section.) The If the detector can discriminate at three levels, the input information that will have to be stored concerning each logic becomes more complicated. Presence may be de• signal is the state and the last time the state changed. There termined on 2 lanes. In the simplest case, the detector are four states—red-green, red-amber, green-red, and am• would put out the information "0", "1", or "2." Thus, the ber-red—but only the times at which red changes to green, computer would have to accept data through a translator on either set of faces, is essential. so that it could add 1 or 2 counts when required. Doubling the storage capacity for the channel would mean that 7 LOCAL CONTROLLER OPERATION binary bits in each word would be used. Computed occu• pancy would be average for the two lanes, because no lane Much or most of the actuation of the traffic signals can be discrimination is afforded by a single loop detector cover• done by fixed-time cycle controllers equipped with a man• ing two lanes. ual control override feature. Determination of volume counts on a single lane can In a typical controller an induction motor drives a dial be made through a logic that requires that two successive through a reduction gear so that the dial makes one revo• "O's" be followed immediately by two successive "I's" to lution for a full signal cycle. Cycle length is determined register a vehicle count. This is consistent with the radar by gear selection. Relative phase lengths for the crossing detection philosophy of "two successive blips on two suc• approaches are determined by the relative arcs between cessive scans," and should suffice for traffic surveillance pin positions on the dial. As each of the pins reaches an purposes. index point it energizes a solenoid that drives a cam A similar logic can be used on a multilane detector. through a ratchet. Appropriate rises or falls on the cam The input will be held over a period of four interrogations, open or close the light circuits when the new index posi• as previously, the logic simply checking that the second tion has been reached. pair is at higher level than the first pair. When this con• It can be seen that the computer can take over the opera• dition is satisfied a volume count is added into the register. tion of the local controller by only two command lines. The volume register need only provide for 1 count per One command signal would change the operation of the second per lane. controller from fixed-time cycle to computer control, or Discussion of the deldt method for counting arrivals and the reverse. The other command signal would take the departures is not treated at this time, nor is the complica• place of the phase change pulse from the manual control. tion caused by analog signature for multilane application By interrogating three of the actual bulb circuits to the of the loop detector. signal faces, the computer can be informed unambiguously At least one other piece of information would come in as to the state of the signal. For instance, if the red and from each intersection. This would be the current status green circuits on one face and the green circuit on the of the traffic signal; red, green, or amber, and the identi• other face are sampled for voltage or no voltage, the com• fying direction. Other information would be forthcoming puter logic shown in Figure B-4 will define the state of for signals operated on cycles with more than two phases. the signal. A logic can be programmed into the computer to determine Other local controllers that might be built on the same the elapsed time for the signal phase on each approach principle (that is, a timing dial and solenoid-operated 29 ARE SIONALS Red 1 & 3 1 & 3 BED Circuit Tes (2 & U No not red) Green 2 & U ^|AR E SIONALS ARE SIGNALS Green 1 & Circuit 2 & U GREEN 1 & 3 • Circuit 7 \ Tes No (Amber) Tes No (Amber) Figure B-4. ARE SIGNALS Red 1 & 3 1 & 3 BED Circuit Red 2 & U_ ARE SIGNAI£ Green 2 & U Circuit 2 & U RED Tesy \No \ Left Turn ARE 1 & 3 ARE SIONAIS ARE SIGNAT£ .Green 1 & 3 LEFT TURN ON 2 & U GBEES 1 & 3 GREEN 14 3 Tes No Tes No Tes No (All Red (AH Red (2ih Green (2&U Amber (1&3 Green (143 Amber 1&3 Left 24U Left 1&3 Red 143 Red Zih Red 2< Red Turn On) Turn On) No Left) No Left ) No Left) No Left) Figure B-5. phasing cam) can be slaved to the computer in the same FIXED AND INITIAL INPUT DATA way. As the complexity of the phasing increases, the For each intersection the following items should represent amount of information on the state of the signal will in• the maximum number of parameters for which values must crease, which will require additional lines or multiplexing be placed in permanent storage in the computer. Some are of tones coming into the storage equipment. For any single geometric (see sketch on next page): case, the best way to transmit the information will be a function of the number of bits coming in and the distance Ji = distance from mid-block detector to stop line, ap• over which they must be transmitted. proach leg 1; For instance, suppose a usual four-way intersection d^— distance to previous intersection, approach leg 1; signal includes separate left-turn phases. Information on /i = number of lanes, approach leg 1 (this may be changed during the day and week if parking rules affect the the state of such a signal would require that two more number of traffic lanes); "bits" than for the ordinary signal be transmitted, one for red on all four faces and one to identify which pair of and others reflect traffic and control parameters: approaches is showing the "turn left" signal. The logic *^G>iiiiii~ niinimum green time, approach leg 1; might be as shown in Figure B-5. "Leading" or "lagging" •^I'liiiax" maximum red time, approach leg 1; green signals might be handled in much the same manner, <^,.,.<,ic = maximum cycle length, regardless of traffic de• the differences being in the lobing of the phase change mand (to check operation of controller in the cam. absence of demand signal); 30 Approach 1 I Approach U Approach 2 ^3 Is I Approach 3 'i> ''i = percentage of left (right) turns from approach special considerations must be included. It is not likely, leg 1 (this figure may be varied with time of day however, that either traffic density or pedestrian volumes and day of week, if not determined by surveil• will be so great in the smaller cities as to warrant the use lance) ; of control doctrines that take into account pedestrian re• Vi = average approach speed, volume dependent or quirements at intersections. computed from occupancy data; Actually, the only thing that will interfere with pedes• <^An,i„ = minimum clearance time to reflect pedestrian trian crossings is a large percentage of turning movements. requirements and/or braking conditions and If turning is moderate, people can make the crossings with local speed limit. the light. Although there may be some slowing of the Departures from these inputs will be required or desired, traffic making turns, assuming that the pedestrian has the depending on the nature of specific intersections. For right of way, the average flow rates for right turns can be instance, the use of an average of four detectors per signal• observed and set into the computer control doctrine as a ized intersection is based on the need for up to six at some performance number. No account is taken of the effect locations and correspondingly less at others. of left turns, because it is assumed that these would be forbidden at times and locations of heavy traffic. PEDESTRIAN CONTROL It is possible that a pedestrian crossing may be required at some mid-block location. The treatment of such a situa• In the most general case of traffic control at an intersection, tion would be to include a manually triggered signal in the if there is no prohibition to the turning movements of system. If the crossing was located in a heavily traveled vehicles, the only way in which passage can be guaranteed street, it would appear to be appropriate to tie the signal to pedestrians is by the use of an all-red period long enough into the rest of the control system. For instance, if the sig• to allow people to walk the longest distance from curb to nals along the street were operating in a progressive mode, curb, which is the diagonal. The pedestrian problem is of the pedestrian's operation of the signal would be restricted sufficient importance in large metropolitan areas that such to signifying a need for passage. The computer would in- 31 elude the changing of the crosswalk signal so that it syn• ment phase, this can be accomplished by an extended all-red chronized as well as possible with the expected gap in the period. Informing the computer of this state will require traffic stream. At times when the signal system is not com• four tones from the controller box. If such a phase is built puter controlled the pedestrian signal could be either un• into a controller that provides exclusive left-turn move• coordinated or tied in with a local progressive controller. ments, no additional information is required, but only a Returning to the idea of an exclusive pedestrian move• change in the logic. APPENDIX C INPUT INSTRUMENTATION REQUIREMENTS FOR A REAL-TIME DIGITAL-COMPUTER-CONTROLLED TRAFFIC SIGNAL SYSTEM To implement the traffic control equations of Appendices nects loop 4 with detector A through OR gate 1. A typical D, E, and G in a complex network of street intersections suggested implementation using relays as the logic elements by means of a centralized computer control it is necessary is shown in Figure C-3. to have some form of information gathering equipment at The instrumentation for detection of the phase state of the critical intersections. This equipment may be divided the signal controller is shown in Figure C-4. Only three into two groups; data collection and vehicle control. The conditions are needed for the complete specification— traffic state at any intersection must be known at all times. detection of green condition on the N-S face, green con• From computations based on this information the com• dition on the E-W face, and red condition on the N-S face. puter sends to the signal control units at the intersections Because the signal controller is either on or off in each control signals intended to optimize traffic flow. case, a binary coding scheme may be used. A phase pat• tern and coding table also are shown in Figure C-4. INTERSECTION INSTRUMENTATION INPUT LOGIC AT CONTROL STATION A general four-way intersection is shown in Figure C-1. This represents the maximum amount of detection equip• The data from each intersection must be transmitted to a ment that would be required at a single installation. Many central control station where the computer is housed. Be• intersections would be of the T or Y type and some would cause all information is of an on-off (binary) nature, a involve one-way traffic. In these instances less detection selective signaling system using telephone lines was adopted equipment would be required. Figure C-1 shows eight as a transmission medium. Each channel of information vehicle detectors, four located at the stop line of the inter• would have a specified signal frequency assigned. At the section and four upstream on the approach lanes to the in• central site tuned receivers would be used to detect the tersection. The detectors are of the induction loop type, information. Each telephone line would then carry a com• which initiates detector contact closure when a vehicle posite of tone signals in both directions between intersec• passes over the loop. To minimize the number of detectors tions and central control. necessary, a time-sharing technique would be employed The information from each intersection is decoded and where the two detectors in the intersection would be grouped into a computer word in the following manner: switched between the four stop-line loops, depending on 1. Bits 1-3 contain the three bits denoting the phase the phase of the signal controller. When the signal con• state of the signal controller. troller was green for the N-S traffic, loops 1 and 3 would 2. Bits 4, 6 contam the time-shared stop line intersection be active; when the signal controller became green for the vehicle detection information. Vehicles are counted only E-W traffic, loops 2 and 4 would be active. The approach in the green phase direction. detectors would be active at all times, thereby providing 3. Bits 8, 10, 12, 14 contain the approach vehicle detec• continuous data on incoming traffic. tion data, which are continuous from each intersection. Figure C-2 shows a typical traffic phase pattern and a 4. Bits 15-21 contain the permanent binary number block diagram of the logic necessary to accomplish the identifying each intersection. These seven bits offer assur• switching function. Loop detector A is connected to either ance that the computer will recognize correctly the data loop 1 or loop 4, depending on the signal controller con• from the individual intersections. dition. If the N-S signal is either amber or green a signal passes through OR gate 3 and enables AND gate 1, thereby Figure C-5 shows the input word structure. connecting loop 1 to detector A through OR gate 1. If The number of instrumented intersections totals 116. the E-W signal is either amber or green a signal passes Data from each are brought continuously to the central through OR gate 2, which enables AND gate 2 and con• control site and the computer control commands are sent 32 APPROACH DETECTOR VEHICLE DETECTORS X APPROACH • DETECTOR s APPROACH DETECTOR • t I AND 3 OR 2 AND 4 TRANSMIT DATA DEPENDING UPON CONDITION OF SIGNAL CONTROL PHASE (GATED BY YELLOW AND GREEN) APPROACH • DETECTOR Figure C-1. Intersection configuration. back to each intersection as required. To get the required of these AND gates goes to another group of 21 AND accuracy to meet the control system specifications, it was gates associated with the appropriate 21-bit intersection desirable to sample vehicle detectors approximately 60 data word. When a particular multiplexer AND gate has times per second. Each sampled input data word is then the correct input it enables the associated 21 AND gates, presented to the computer input terminals for approxi• and 21 bits of data for that intersection are presented to mately 144 /isec (microseconds). This is the multiplexer the computer input lines through multiple input OR gates. period; the product of the inverse of the sampling fre• These OR gates have 116 inputs and provide the connec• quency and the number of sampled intersections (T = tion between intersection data lines and the computer input 1/60 X 1/116). Figure C-6 is a logic diagram of the input lines. circuitry. The basic clock frequency of the chosen com• puter is 500 kilocycles. This is divided down by a factor of 72 to arrive at the multiplexer gating frequency (6,941 OUTPUT LOGIC AT CENTRAL CONTROL STATION cps), which approximates the product of the sampling fre• Figure C-7 shows a logic diagram of the output circuitry. quency and the number of sampled intersections (60 X The output control signals from the computer are generated 116). This in turn drives a 7-bit counter, which resets at a rate of one every 2 sec. They consist of a HOLD com• after 116 counts. The true and false outputs of each flip- mand and an ACTUATE command. Each consists of one flop in the counter provide the coding signals for 116 bit in the output word structure. Bits 3-9 are the inter• multiplexer AND gates. Each of these gates has seven section identification information. There are 116 selector input lines from the counter and one input from a delayed AND gates which have 8 input lines each. Seven of the gate pulse to allow the counter lines time to recover from lines connect to the intersection identification bits in the the transient switching conditions. The output from each output word. The eighth input is derived from a computer- 33 generated Read pulse gated by the Actuate command. The duration to cause an actuation command at the remote output of the selector gate provides one input to 3 AND signal controller. A duration of from 300 to 500 milli• gates controlling the HOLD and ACTUATE signal cir• seconds is considered sufficient. This pulse is transmitted cuitry. When it is desired to transfer a signal controller at to the intersection and actuates a stepping circuit in the a particular intersection from fixed-time operation to com• signal controller which changes the phase. To return a puter control, the output word presented by the computer signal controller to fixed-time operation the HOLD bit will contain a binary 1 in the HOLD bit and the correct becomes binary 0. This enables an AND gate connected to 7-bit intersection data. The HOLD bit enables one input the Reset input to the hold circuitry flip-flop. The next Read to an AND gate driving the Set input to a flip-flop circuit. pulse then resets the flip-flop and the controller is released The Read pulse provides the trigger signal which sets the from computer control. The computer will evaluate each flip-flop. The flip-flop output is then transmitted to the of the 116 subnetworks in sequence. Actually, the decision intersection, transferring signal controller operation to the computer. If it is now desired to change the controller of the phase change will be dependent on the value of the phase state the ACTUATE bit becomes binary 1. The objective function (i.e., relative delay) at any given time, Read pulse now goes to an AND gate triggering a multi• determined by the current and predicted traffic flow in the vibrator, which generates a control pulse of long enough system (Appendix F). TRAFFIC SIGNAL PHASE PATTERN LEOS EW LEGS NS G ) LOOPS > 2 & 4 Y I ACTIVATED AND GATE R LOOPS I & 3 OR GATE R :i ACTIVATED :0r LOOPS T.G. = TONE GENERATOR 2 & 4 ;! ACTIVATED LOOP LOOP DETECTOR A T.G. 1 LOOP 4^ 4^ ^EW ^EW ^NS •^NS CONTROLLER PHASE GATE LOOP LOOP DETECTOR ) / B T.G. LOOP Figure C-2. Time-sharing vehicle pickups using signal controller phase as gate. 34 RELAY DETECTOR TUNING #\ RELAY 2 TUNING m RELAY 3 TO RELAY POWER DETECTOR B TUNING #3 TUNING #2 2 RELAYS - TWO-POLE DOUBLE-THROW I RELAY - SIX-POLE DOUBLE-THROW Figure C-3. Suggested hardware for time-sharing vehicle detector units at intersection. SYSTEM INSTRUMENTATION COST An investigation was made with reference to the sources of supply for the instrumentation required at each inter• section and at the central site. Based on the mode of operation desired, a typical set of equipment cost figures was compiled for the complete installation. The breakdown was as follows: Intersection equipment, ^ $1,575 $182,700 Input logic interface at central site 26,530 Output logic interface at central site 19,740 Telephone line leasing 2,000/mo. Total $228',97d plus $2,000/mo. These figures are approximate, as telephone leasing rates will depend on the community selected. Not included are the maintenance and construction costs associated with the equipment's installation and upkeep. Figure C-4. Monitor for phase condition of signal controller. ASSUMING THAT NO SIMULTANEOUS T G. R^j-R^yf CONDITION OCCURS MIXED T.G. OUTPUT "HS SIGNAL CONTROLLER PHASE PATTERN T.G. T.G. = TONE GENERATOR NS EW BINARY CODE OCTAL EQUIVALENT OF R G BINARY CODE "NS ^NS ^EW R Y I CYCLE G R Y R R G R Y G R 0 0 Y R TYPICAL INTERSECTION INPUT LJLJL JL JL JL J. TONE T. T. T, T. T. T. T. rnrREC. R. i R. R. R. R. R. R. (SIGNAL PHASE STATE) (D, OR Dj) (Dg OR D^) (D5) ("6) ("V) (Og) GATE I-II6 ' YY V Y Y Y Y Y ( INTERSECTION IDENTIFICATION TAG 1-•116 ) ^ ^ ^ ^ ^ I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 2! INPUT WORD STRUCTURE D,'D3 Dg Dg D7 Dg ^ SIGNAL OR OR INTERSECTION NUMBER CONDITION Dj D^ EACH INTERSECTION DATA TO BE SAMPLED SEQUENTIALLY APPROX. 17 MSEC. SAMPLE TIMING INT I INT Jl_ -5iL T.R. = TONE RECEIVER 4> AND GATE Figure C-5. Central site input logic. (Di, D2 Ds —I I 16 represent the possible eight detectors located at an inter- I I section.) •wojSaip 31S0J jojtuoo tndino aililiANI = I il3UIHSNVill 3N01 = 'I'l 31K jainduioj 7-3 sunilij i3S3!l = !l HOlVHSIAInnH lOHS 3N0 = "S'S 13S = S 911 -INI 911 -INI Z -INI I N0li33S)l31NI -4- •1 •i •i •i 'NVUi 'Nm 'NVill •i •1 •i •1 3N01 3N01 3N0i 3N01 •S'S I 911 31V9 911 31VS I 3iVS I 31VB 31V9 QNV 80133135 rrrn I I II I I I I I I I I I / 9 s 11 e z I i 9 S I1 E Z I Z 9rr 9 11m e Z I / 9 s ti e z I 3sin N0imidllN3ai N0I133S)I31NI I iig 91 lis e iig z lis il3ljn 11 111,, I....I I I ; 11....111 I I....I I 911 sii ti e z 511 9 ti e 911 911 sue 911 SI I 9 ti e sindino \i 01 91 911 'INI I -INI I KOI103Sil31NI 911 31V9 SII 31V9 E 3iV9 I 3iVB I 3i»0 3iV9 ONV a3X3idinnw II I ! I I II 'a 'I I! I I I I I I I I I I I I , I I I I I I I 3 4 is p * i ^9siiezi' Z9stie:i ZiStlEJI Z9S1ieZI ' ^SSIlEJl A»i3a I i I M i I H 9 M I H M i I M ? I I i I ; I ii3iNno3 xia z •luvjSvtp JtSoj J0JIU03 fndut a/w {VJjuao jaindwoj -g-j aunSij 9-f- KOOIO OH OOS 37 APPENDIX D DERIVATION OF A MINIMUM-DELAY FUNCTION FOR AN ISOLATED INTERSECTION WITH SIMPLIFYING ASSUMPTIONS It has been estimated that more than 75 percent of vehicular vehicles, pedestrians, weather, etc., is monitored (within delay in urban areas can be attributed to intersections in the limitations imposed by the detectors employed) with general. However, due to the geometric grid network and the computer operating on the dynamic and static informa• the associated volumes of vehicles, such areas contain a tion and the resultant signal display relating the decisions high concentration of signalized intersections. Without to the motorists and pedestrians. The advantages and changing the physical characteristics of the network, the limitations of any such system (in vehicle-seconds of delay efficient operation of these signals then becomes a major saved) is difficult to evaluate analytically. Specifically, it factor in the reduction of the avoidable delay. is suggested that the relative merits (when compared to The primary function of a traffic signal at an intersection less costly alternatives) of a particular system, be evalu• ated by computer simulation techniques (accounting for is to regulate capacity (assign right-of-way). Selection the limitations inherent in any model). The ultimate test, of proper cycle lengths and splits for these signals is at of course, is in its application to the actual city being times critical and in general necessary if service to the studied. motorist is to be optimized. The term "optimization" in this context is used to mean the minimization of the motor• Another approach in the synthesis of such a system is to ists' travel time or delay (i.e., time necessary to travel a program the computer to simulate discrete traffic control given route in excess of that required for "free" vehicles). techniques as currently employed by individual specialized systems (e.g., progressive movement, linked volume-den• The existence of such a delay, as defined, is inevitable with sity, etc.) With this method, the computer would neces• the current static network (e.g., physical characteristics, sarily be capable of assigning various control subroutines single level intersection). to different intersections as dictated by traffic flow (sen• Numerous attempts have been made to solve the signal• sors), time of day (clock), or the decisions of a human ized intersection problem. Hence, there are currently many operator. Heuristically it appears that the more general types of specialized traffic signal equipment and systems approach proposed here (i.e., the implementation of the whose purpose is to "expedite" traffic through urban inter• basic criteria in the form of a set of equations), would be sections. Although many such systems have produced good the most flexible of the two methods, and in general would results, others have at times systematically aggravated have the smaller reaction time to changes in traffic de• rather than alleviated a specific traffic problem. In any mands. case, specialized systems implement discrete control phi• Currently, researchers are experimenting with each of losophies which are artifices employed to obtain the mini• these general philosophies (i, 4). It is hoped that they will mal-delay results and are too limited in adjusting to the be able to contribute to the evaluation of the relative ad• rapid fluctuations of urban traffic. To obtain a more de• vantages of the two approaches. sirable system having the sensitivity and flexibility to react to the uncertainty and variability of traffic flow that occurs within the time intervals of practical signal phase lengths, DERIVATION WITH ASSUMPTIONS it is proposed that a computer directly implement the basic The starting point is observation of signalized intersection delay criterion. Logically, the control decisions should A, which may be assumed independent of any other inter• result from the continual sampling of the traffic flow char• section (i.e., isolated). With the proposed control system acteristics and with such speed as to gather the pertinent the digital computer is periodically fed information from data, calculate the decision, and actuate the controls in real remote sensors that serve to sample the dynamic state of time. To process the large quantities of data within the the intersection. Based on the minimum-delay criterion, required time intervals, the system will be synthesized em• the system uses all pertinent information (e.g., updated ploying a high-speed large-scale digital computer. Infor• detector information, and information from the computer's mation describing the traffic flow and signals displayed will permanent memory) to make a decision as to which signal be fed into the computer from strategically located detec• display would be optimum. As a result of these computer tors. The detectors may measure the number of vehicles, calculations, local signals are controlled by actuating relays speed and/or presence to convey the "state" of the net• at the particular intersection through the system's com• work to the computer. The computer, working in real munications network. For the present example it is as• time through the programmed equations implementing the sumed that only signals indicating stop (red), go (green) minimum-delay criterion, will compute the best set of sig• and clearance (amber) are available for display to com• nals at a given time for the entire network. plementary traffic (e.g., north-south or east-west). Hence, Hence, the proposed system may be viewed as a servo- exclusive pedestrian phases, turning arrows, etc., are not mechanism (Fig. D-1) in which the dynamic network of included. 38 COMPUTER: Programmed equations Memory static characteristics, etc. DETECTORS SIGNALS NETWORK (DYNAMIC) Figure D-1. Traffic control loop logic flow diagram. The traffic signal's phase length, although flexible and result of the delay saved due to the departing vehicles dur• under the control of the computer, will be bounded by ing the proposed extension; the second term, 5,^, is the practical limits for minimum green time, (/)GiK,w,„,„. and resultant savings that accrue to the vehicles forming in a maximum red time, I^KIX.S,, Within the "limits * queue behind those departed and are served by the inter• Ar<^(:iK.w,„,,,-0,(;li;.w-<^ The 5„ term of Eq. D-1 expresses, in vehicle-seconds, another factor D,„„.„, must be included, representing the the delay saved which accrues to those vehicles served minimum number of vehicle-seconds required to traverse earlier in time as a result of the previous departures. The the distance corresponding to the application of the delay term must therefore calculate the total number of arrivals equation. Hence, during the next phase, 0UIE,W. pl"s those remaining in D (D-9) queue, and multiply this sum by the time the vehicles are TH • nearer to service. Hence, Eq. D-9 expresses the delay experienced by vehicles on the south leg due to the additional time necessary above that {D-3) normally required to travel the same route unimpeded. where The duration of the queue on the south leg, kgAt, as a result of changing the phase to <^(JIK,S immediately, may be AV= y ««.;Af.) + Af„o J - (D-4) found by solving Eq. D-10. The number of vehicles in queue at the start of the new phase on the south leg is given by Njn, and a,s and are the arrival and departure rates, 5) respectively, for the interval At,; that is. -\i=i / J "LV ''lE. "iw = arrival rates, in vehicles per second, on the Nr .+ '^a,^At,- J d'.sAf,^0 (D-10) east and west legs, respectively, the numeri• cal values, measured and/or estimated for where *s 's the smallest integer to satisfy the inequality. the / th interval, being constant for A<,: Note that the departure rate rf',}, (e.g., saturation flow) ^E. = estimated departure rates, in vehicles per occurs only after an elapsed time of /y representing the second, from the east and west legs of the assumption that the time lost in the starting transient may intersection during the proposed extension, be represented by a period, /«, of zero departure rate, in• stead of in actuality being distributed among the first few 5x,+E. di*xv = estimated departure rates, in vehicles per departing vehicles. second, from the east and west legs during If, however, the start of the <^(;|x,s phase is postponed by the initial portion of the next phase, (^(;IE,W'> a period At, the depletion of the new queue on the south ^rE, ^iAv= residual queues on east and west legs, in leg will occur at time k'^At. Where k' is the smallest integer number of vehicles; to satisfy •^ijii, "^jw = delay saved on the east and west legs as a result of the vehicles being served nearer to Nii,+ ^a,^At,~ d,^At,^0 (D-11) the start of the next green phase, GIK,W; (<^>UIE,W + <^'AIE.W + 'n,w) Similar equations exist for the extended queue duration L = (D-6) for the north leg. Hence, the additional time (relative to calculated to the nearest whole number. the alternatives) of the existence of the south queue A^,s is given by The total saving, in vehicle-seconds, may now be written as At„s = *'sAf - *sA/ (D-12a) (D-7) or or At,s = At(k'^-k^) (D-12b) •SriE.w — MEA' + dyf^t) ($uiE,w + ^'AIE.W + 'E,\V)] and the similar equations for the north leg yield At, At (*'n - k^) (D-13) Although all vehicles required to stop at an intersection will suffer a delay (when compared to a free-flow condi• (D-8) tion), only tho.se vehicles impeded by the extension Ar, will be considered in the relative delay calculations of the The next calculation is to determine the delay, Dji^. and D,,,., and D,„,. terms. If it is assumed that all vehicles have Drs, caused to the vehicles on the north and south legs, similar deceleration and acceleration characteristics, both respectively, by deferring the start of phase where the summation of the arrivals, fljg, between the Hence, the relative delay equation is limits kg and k'^ yields the additional stopped vehicles on the south leg. Note that it has been emphasized throughout this de• velopment that for the purposes of control decisions the -,a,-d,)-^:^At,j^- programmed equations should be relative in order to ob• tain the best solution from the alternatives (i.e., difference in delay occurring in changing the signals immediately or E{ Nr, + ^(a,-d,)At, at a time At later). -(a,-d,)^ A/,|^ (D-18) Now examine the term D^, expressing the difference in vehicle-seconds suffered in the queue for the two alternatives. The number of vehicles in the queue, N, in which all parameters within { }g apply to the south leg, in genei'al may be expressed as a continuous function of the terms with the unprimed subscripts apply to N(t) of time N(t). This representation is physically realistic, as Figure D-2, and those with the primes refer to N'{t). The vehicles do not jump out of or into queue, but rather flow summation limits start at /=1, hence the unprimed de• (e.g., % vehicle per second). Hence, Figure D-2 may parture rates, di and represent the distribution of the express the general queue size at an intersection for two aforementioned lost time, Zg, within these terms*. specific cases (i.e., the two alternatives), where N(.t) rep• As an example in applying Eq. D-18, let it be assumed resents the length of the queue for the case in which /"I'lt /"lit the east leg to zero. Dg= I N'(t)dt- j N(t)dt (D-16) Since the delay equations for the other legs (north, east, and west) are similar, they will not be presented here However, to apply Eq. D-16 to the proposed system the in detail. integration must be performed numerically. If the assump• Let it be assumed that a specific physical condition exists, tions implied in this case by the sampling rate 1/Af (i.e., in order to indicate the manner in which a decision may that the predictions and/or measurements of the arrival be made employing the previously developed equations. and departure rates are constant over the period At) are Suppose that the east and west legs are receiving the red included, the exact integral, in numerical form, is obtained phase, iiiE,w. the minimum green time, <^Gix,Sn,io has in Eq. D-18. The form of Eq. D-17 derives from the fol• elapsed. Then the computer's decision to change or extend lowing: At any time }At, the number of vehicles in queue, the current phase by At must be based on the minimum- Nsj will be the initial number, Nj, less the integral of the delay criterion, assuming also that the current elapsed departure rate minus the rate of arrivals over the period green time, <^iGiN,s. is less than Figure D-2. 41 It 6 — 0, the signals should be left unchanged because less lost time attributed to the initial ac• or equal delay would be incurred by an extension of the celeration period to east (or west) <#>GiN,s> RiE,w phase. However, if 5 < 0 a greater delay vehicles; will occur if the signals are changed At later. This latter total amber phase, in seconds; test is not sufficient to terminate the current phase immedi• 'A- portion of the amber phase that may ately, because calculations of d^i^,, ^SA*. • • •. OnM i"ay be considered an extension of the red yield a g-value algebraically greater than e^f The mathe• phase; matical and practical limitations on the number n that may an estimate of the term to which it is be employed and produce meaningful results depends on applied; the detectors (type and locations), current traffic char• «.E. fllW = arrival rates, in vehicles per second, on acteristics, the estimators employed, and the upper limit the east and west legs, respectively; <^G1N,S • must accelerate to free speed; signal to the east-west and north-south D„ = a component of Dy, attributed to the legs of the intersection, respectively; BiE,w> ^HiN.s = that phase which displays the red sig• delay suffered while in queue; nal to the east-west and north-south a component of Oj., representing the legs of the intersection, respectively; vehicle-seconds required to traverse the minimum amount of time a green unimpeded the path to which the delay phase must receive before the phase equation is applied; may be changed by the computer's departure rate, not including the lost decision; time (i.e., excluding acceleration (from the maximum amount of time a red stop) transient); phase may receive before it is changed length of queue (number of vehicles) by the computer, independent of cur• at the start of the new phase; rent traffic demands; k, k' = integers representing the number of <#>iG> <^il elapsed time of the current green and intervals, At, until the queues are ef• red phases, respectively; fectively dissipated (for the two al• with respect to intersection A; ternatives); ; unit of time considered for the pro• At-- additional time (relative to the alterna• posed extension, and 1/Af is the re• tive) that the queue remains; sultant (network) sampling rate; constants of proportionality for Da„ : total delay saved to the east-west >riE,w • and Di„.e terms, respectively; traffic; queue lengths (number of vehicles) a component of ST, attributed to the N(t),N'U) = for the cases where the phase is expected departures; changed immediately or at an interval i a component of S^, attributed to the At later, respectively; number of vehicles serviced earlier in time; d^r, Atf •• referring to iV'(0; and 6M a quantity employed to test for mini• d^.,E> d" W departure rates, in vehicles per second, from the east and west legs, respec• mum delay between the alternatives of tively, during the proposed extension, an immediate change in signals or a A/; postponement of A*. 42 APPENDIX E DERIVATION OF A MINIMUM-DELAY FUNCTION FOR A SUBNETWORK OF SIGNALIZED INTERSECTIONS The minimum-delay equations developed for signalized is decreased as a function of the distributions of the turning intersection A in Appendix D do not account for the delay movements at each intersection. Further, one may examine experienced downstream by those vehicles released from the situation whereby turning movements are prohibited A. Although these isolated-intersection equations are ap• and the arrivals at a point downstream are certain, but are plicable to all situations in which the state of the down• dispersed only by the variance on the mean velocity, which stream network may be neglected, the vehicular arrival has associated with it the variance of the arrival times, rates to A, a„ may de dependent on a neighboring upstream accounting for the distance traveled. With the inclusion of signalized intersection (see Fig. E-1). In this case, the one signal, or even one stop sign, controlling another inter• predictions, a„ will reflect such influences. section between the intersection being evaluated and the The choice to neglect a certain portion of the surround• one downstream, the standard deviation of the predicted ing network with respect to the decision to be made at arrival times may be greater than the duration of the green intersection 2 (Fig. E-1) is a logical (practical) assumption phase (for the downstream signal), thus introducing a and as was shown does not imply that such an intersection significant error in the predicted delay. is literally isolated (i.e., does not influence or is not in• For practical reasons, such as those described, network fluenced by conditions at other intersections). It does, equations will generally be limited to the immediate neigh• however, indicate that the intersection is being treated in boring (minimum interference) signalized intersections, such a manner, because the vehicles may have to travel normally consisting of four pairs of intersections each con• relatively large distances before reaching another point taining the intersection being evaluated. (signalized intersection or measurement station), or pass through a number of unsignalized (non-instrumented) GENERAL PROBLEM STATEMENT minor intersections before reaching a major intersection, or travel a relatively short distance where there may be a This appendix develops a set of general equations to mea• significant amount of friction (e.g., sinks and/or sources), sure the relative delay to vehicles currently being controlled or any combination of these conditions. It should be noted at intersection q, that will include the predicted delay when that in all the aforementioned instances it may be possible these vehicles reach downstream intersections r, s, t, and u to say with a high degree of certainty that the vehicles (Fig. E-2), for the control alternatives assumed to be avail• will arrive at a particular point; but when in time (e.g., able at q. Although the minimum-delay solution is sought during which cycle or even which day) they will arrive has in terms of the five intersections of two two-way streets, associated with it a very large uncertainty. In such in• it is realized that many other network configurations are stances it is apparently futile to link the intersection being possible. However, the most common ones will simply be evaluated with the neighboring ones by estimating the delay modifications of the foregoing subnetwork. incurred at the signalized intersection downstream from The problem is to decide on the "optimum" time to the released vehicles. However, in urban areas, and in par• change the signal at q, assuming a symmetrical signal dis• ticular within the central business districts, such isolated play, where "optimum" signifies the minimum aggregate intersections are in the minority. This is basically attributed delay accrued to those vehicles being controlled at inter• to the geometry of the grid network (e.g., city street dimen• section q. sions, and layout), and the vehicular and pedestrian vol• The current conditions at q and the state of the rest of umes attracted to the area, which necessitates a high den• the network (e.g., particular phase, phase time elapsed, sity of signalized intersections, and the more or less ordered queue lengths, approach rates, departure rates, and various flow of traffic which is prescribed by the enforcement of predictions based on past measurements) will be used to various traffic ordinances (e.g., parking, turning move• implement the minimum-delay criterion. The solution, for ments, speed limits, one-way designations). the most part, is based on the general development of the A question which logically arises at this point is: How isolated-intersection model (Appendix D). Although the many signalized intersections downstream from the vehicles isolated case was concerned solely with the delay associated released from the intersection being evaluated, should be with intersection q, the equations are here being extended considered in the network delay equation? In the most by considering the delays incurred in the subnetwork con• general case of an intersection of two two-way streets (with tained within the dashed lines of Figure E-2. no turning prohibitions) each vehicle has the choice of First let it be assumed that the signal at q is green to three paths (straight through, left, or right turns). As the east- and westbound traffic (west and east legs, respec• number of intersections being considered is increased, the tively); namely, phase „ <^,;IK,W (q i{i.\,s)- Hence, it must probability of the released vehicles reaching the farthest be decided whether the current phase should be extended intersection downstream (in the original direction of travel) by HA/ or terminated immediately (i.e., ,j GIX,S 43 J NEGLECTED NETVWRK IN o- MAKING A DECISION WITH ( RESPECT TO SIGNAL @ SOURCE OF ARRIVALS"/! TO WEST LEG OF ® Figure E-1. Intersection of two one-way streets. initiated). To evaluate the alternatives, the delay accrued N by the vehicles up to the time that they depart from the i subnetwork (at the perimeter of the dashed enclosure) must be considered. The implementation may take the form of evaluating either the difference in times of service at the perimeter (exit of subnetwork), or the sum of delays incurred at each intersection along the route. The latter approach is pursued here. Hence, the total relative delay T^/i I or savings will be considered as the sum of contributions, from at most two signalized intersections for any particular vehicle. Therefore, the 6„sr^eTm for the isolated inter• 1 section (Eq. D-19) is applicable to the total development -I and is the starting point. SAVINGS WITHIN SUBNETWORK LU_i The SriK,-w term (defined by Eq. D-7) is only a part of the total savings within the subnetwork, as this is the savings Figure E-2. Subnetwork (q, r, s, t, u) of of delay at intersection q only. The additional relative sav• signalized intersections. ings within the entire subnetwork is expressed as the sum of the individual savings at each of the neighboring sig• nalized intersections, as follows: "V = (...rS + ...sS + a..S + „.«S) (E-1) or after being held for the duration of the next red phase, In this notation, the first pre-subscript, q, refers to the •1^1111: w- The expression for the q, r intersection pair is situation whereby the savings equation compares the rela• tive benefits of the alternative decisions to be made at "^'[„,,S = „,,D^KiK.«-„,^"] (E-3) intersection q; the second pre-subscript refers to the inter• where section within the subnetwork where the saving occurs. Further, the ,,5' term does not express the total* relative ,, ,.D''''H|I.; IV = the (estimated) delay incurred at r, to the savings within the subnetwork q, r, s, t, u. This term is vehicles released from intersection q after denoted by "-^',,5, where waiting for the next red phase, q<^niE,w. ^nd choosing their path through r; and "V ="^'(„5' + ,Sr,K,w) (E-2) „ ..D" = the (estimated) delay incurred at r, to the and „5r|,,;.,v is defined by Eq. D-7. It is desired, now, to same vehicles that are released during the express each of the contributions to "-^',,5' in terms of the current proposed extension and also desire difference in delays (i.e., vehicle-seconds in addition to service at r. those necessary to travel through the subnetwork from q Similar equations may be written for the relative saving unimpeded) suffered at the neighboring intersections, which at s, t and u. would occur if the vehicles are released as a result of the extension of the current green phase at q by nAt seconds, TURNING MOVEMENT CONSIDERATIONS • This value may be either positive or negative. If it is negative, more de\ay is predicted to be incurred by the vehicles from the east, west legs of From Figure E-2 and the assumption of the initial state q, at the neighboring intersections r, s, t, u, if released during the proposed of q (i.e., (^jGiK.w. it|x.s)> 't 'S readily observed that the extension, nA/, than if held at q for the subsequent red phase, „ west legs, implying right- and left-turning movements, re• SAVINGS EXPRESSED IN TERMS OF RELATIVE DELAYS spectively. Hence, in order to predict the total relative It is now necessary to examine the q rD^mit.w and q,rC savings, ,^S, within the subnetwork, and the total relative terms of Eq. E-3. Referring to Eq. D-9, the required terms delay, „D, it is necessary to estimate the proportion (prob• ability) of the vehicles that choose a particular direction may be expressed as from those which are available to them at q (i.e., the three alternatives, left turn, right turn, or straight through). The "^'q,r{£>.kH.. + £>, + i>,.«. - Z>„„rm}s'*>'l«.«- (E-8) estimates of the proportions of turning movements* from each of the legs at q are defined as follows: and "^.r^'s" = "^'q.r{0..... + D, + D„,., - D„„„4s» (E-9) qjc,B = estimate of the proportion of left turns from the east leg of intersection q during the ith interval; in which the superscript and subscript notation follows the ^y,,,, = estimate of the proportion of right turns from the pattern ^4,r,{^s„'i}ii,7''. wherein the various elements are as east leg of intersection q during the rth interval; and follows: qZiB — estimate of the proportion of straight-through's from 1 = decision interval, in seconds, currently being tested the east leg of intersection q during the ith interval (i.e., extend current signal state by this value or (i.e., „z.,.; = 1 — q(J+ y)i.;). terminate immediately), where the value may be Similarly, one may define the estimates of these propor• Af, 2\t, . . ., KM. tions at intersection q, from the west, north, and south legs. 2 = time of start of next green interval as displayed to The vehicles predicted to be "customers" for service at legs 6, 7, referenced from current instant, where r (during the proposed extension of the qi^oiE.w phase) the value may be 0 or (or S"'' nAf). result from the sum of the left-turning movements from 3 = leg at which delay, D, is accrued (i.e., N, S, E, the west leg (eastbound) and the right-turning movements orW). from the east leg (westbound). To arrive at this expres• 4 = intersection at which decision is to be made on the sion, the departure rate is multiplied by time, and also by state of the signal. the estimated proportion for the particular movement. 5 = intersection, within the subnetwork, at which the Hence, delay, D, is accrued. 6, 7 = legs at intersection (4) which contribute to 4S. n 8 = component of delay (i.e., dec, acc, q, norm, or, if '^.r^Hx, y) = 2 ^'•^•^V q^iW Af.} 1=1 deleted, the sum of components). n Substituting Eqs. E-8 and E-9 in Eq. E-3 gives + y{J.n.AKM} (E-4) -^'...^ = »%,,{(D,„.,'i»i.,K,w - /)„....") where '"**„,,./4"(JC, y) is the prediction of the number of -I- (0,/HIK,» -D,") 4- (A,>.>K,« - D„.,<.») arrivals at r resulting from the extension, n^t, of the cur• - (Z>„.,n„^H|«,» - D„.,™,'') }s (E-10) rent signal phase at q (i.e., „(j|i,;,w). In like manner the prediction of the number of arrivals to Inasmuch as the normal (unimpeded) time to travel from each of the neighboring intersections is obtained, as fol• intersection q to intersection r remains unchanged with lows: time, the !>„„„, terms are assumed to have negligible affect on the solution, because they will differ only with the variation in queue size (e.g., D„„,/Rm.w D,,,,,,,,"). This "^'.../IHz) - {qZ.w q5,w AM (E-5) assumption reduces the fourth term of Eq. E-10 to zero. n DELAY SUFFERED IN QUEUE The second term on the right-hand side of Eq. E-10— n namely, „ ,.(D/mi!,» — £)„'')8—expresses the difference in X {ay.w..5.wM} (E-6) i=-L delay suffered within queue on the south leg of intersec• tion r. The vehicles considered are those predicted to be ''\.,,A«(z) = J {qZuo Av. A',} (E-7) released from the east and west legs of intersection q during the current extension and the same vehicles whose where «%.,^"(z), '•\,tA''(.x, y)."^..^''iz) are the pre• departure is deferred by „ arrives at r and ends when the last vehicle arriving from q from the instant that the first vehicle arriving from inter• is released at r, or until the time of the queue's dissipation section q (as a result of the current extension) joins the (whichever occurs first). Hence, the delay to the vehicles existing queue at r, until this existing queue is served. initially queued on the south leg of intersection r, at the Since ^N^" is defined as the number of vehicles in queue time of the first arrival, should be subtracted from the on the south leg of intersection r at the time of the first total delay experienced in the same queue. arrival from intersection q, Therefore, rN,g'>-^A^At, = 0 (E-18) "^..0,.,"= J^„A\"^'N,sj" + J^{(S\-d,)At,} - in which the departures from the south leg of intersection r, rd,»At„ are considered to be summed from the same lower limit (/=!) as the summation of the arrivals, f^^^r-j,Cd,At,) + d, -' At\ rflisAf,, in Eq. E-13 were. Substituting average values for the estimates and rearranging terms gives (E-lla) (E-19) in which a\, the arrivals at r, are considered to reflect only and those contributions from intersection q during the immedi• ate extension. Therefore, if M"Ar is defined as the interval of time over which departures from q during nAt arrive (E-20) at r, The r^siE.w" limit of Eq. E-lla is now examined in .1/0 .1- detail. First, r'^siE.w''Af is defined as the interval of time, referenced from the time of the first arrival to r's south leg, 1=1 1-1- until the queue on this leg is dissipated* or until the last where the summations yield the same number of vehicles, vehicle being considered from the east-west extension at q although the summations occur at different times as denoted is serviced at r, whichever event occurs first. Second, by the minus superscripts on the limits (i.e., the departures r^sin,w"'A' is defined as the interval of time, referenced from intersection q occur earlier than their subsequent from the time of the first arrival to r's south leg, until the arrivals at r). Further, in general, M" # M, which allows queue on this leg is dissipated. Then for the variation in velocities between first and last vehicles considered and also for the fluctuating queue length on the south leg of intersection r. «^'rAfis''+ 2 ,(fl,s-5,s)Af, = 0 (E-21) Therefore the following conditional expressions can be 1=1 written: and substitution of average values for the estimates gives If "^'..^.s" + ,.(5. - rf.)s ./Cs,K,^v°'At = 0 (E-22) l^i^A/" (E-12) from which then (E-13) I'^SIE.1^ W 0' —. (E-23) r(fl-rf)sAf If If r^siE.w" Af is defined as the interval of time, referenced (E-14) from the time of the first arrival to r's south leg, in which then the last vehicle being considered from the east-west exten• (E-15) sion at q is serviced at r, Substituting average values for the individual estimates obtained per time interval in Eq. El\b gives 1=1 ,a,sM«Af = (x^.v^'.w + y>MnAt (E-16) and substitution of average values for the estimates gives where the bar notation implies the average value of the "•^'r^is" + ,5s'""A< - ,5s ,/Csii.:,w""At = 0 (E-25) particular quantity, taken over the intervals A/»A< and from which nAt, respectively, and it is assumed that the interval A If leg of r due to the extension of the current phase at q and the first arrival from the same legs at q due to the termina• r^SIE.w" (E-27) tion of the current phase (i.e., deferred in time). then To clarify this definition and develop an expression re• r^SIW,E° = r^SIE.w" (E-28) lating a to defined physical quantities, the following dis• cussion refers to Figures E-3 and E-4. However, if The shaded vehicle is the same one m both Figure E-3 r^RIE.w" r^SIE.w" (E-29) and Figure E-4. However, it is released (^K'E.W + <#>'A) then seconds later in Figure E-4 than in Figure E-3. Assuming an average velocity from the time of departing intersection (E-30) r^SIE.w" = r^RIE.w" 1 to falling in behind the last vehicle in the queue, the Now that the delay suffered in queue on the south leg of r travel time to fall in place in queue for the two alterna• has been estimated for the alternative of extending the cur• tives may be expressed as b/ V^^g and b'/ V'^^g, respectively, rent green phase, a prediction can be made of the delay where and K,,vg represent the average velocity within that would be incurred in queue to these same vehicles at b and b', respectively, and b and b' are the respective dis• r, after being held for the next amber and red phase tances from intersection 1 to the end of the queue at the (<#>'AIE,W + <^KiE,w); namely, ^D,/'iitK,v. The expression, time of the first vehicle's falling in behind the last vehicle. similar in form to Eq. E-lla, is Hence, the delay expressed in queue, D'>r, will apply b' b 2 {(5'. - d,)^h} - (a, - d,) ^ AtX - R + <^A • \' avp ' nvg/ Ulta J ) s (E-32) Af m*n + a /r By expressing relationships analogous to Eqs. E-16, E-18 and E-19, E-21 and E-22, and E-24 and E-25, the following (=1 r IL (E-31) parameters may be arrived at, respectively: ix,^^•d,^y + y,yd,y;)n in which the lower limit on the summations indicates that (E-33) the delays to the vehicles are considered later in time than Eq. E-lla, and aAt is defined as the interval of time which m<'s — ~ (E-34) is estimated to elapse between the first arrival on the south vd.aAt ® Figure E-3. Prediction of length of queue at point 2 (west leg) b/V,,,,. seconds after decision to extend 0c E «. i Figure E-4. Prediction of length of queue at point 2 (west leg) b7V'.„B seconds after start of deferred r'^SlE.W* ' (E-35) ,(ai-rf,)sA/ r^SlE.w'''"" — (E-36) ''^',,rO.„.. s" = (^K, ^ «,Af,^^ (E-43) ,dsAt where the time averages are assumed to be of the estimates In the case of Eqs. E-42 and E-43 the queue is assumed to per interval over the appropriate (time-deferred) interval. be dissipated over the interval (M" — K"')At. Therefore, the arrivals during this time sXi^/s-^'i/ are assumed to DECELERATION AND ACCELERATION TERMS accrue zero delay in terms of D,,,.j.", D.„.,." and D,^". The next step is to return to the first and third terms of Eq. Equations analogous to E-39 through E-43 may be writ• E-10 and investigate the delay incurred by the vehicles being ten for the alternative of terminating the current phase at considered during their deceleration and acceleration states. intersection q. Hence, the delays would be predicted for Two cases are examined. First, if there is no queue the same vehicles, under the conditions that are anticipated predicted to be formed on the south leg of intersection r, after the vehicles are required to wait for the subsequent at either time of the two alternatives, the relative decelera• red phase, „(/)UIK,\V. These quantities are denoted by the tion and acceleration delay terms will be zero. This implies previously deferred D.„.,^nii;,», D,,,.,.'/'IIIK,» terms. that the relative level of service between q and r is such that no queue exists during the entire time over which arrivals are considered at r. DEUY PREDICTION Second, if a queue persists during both alternatives, there Up to this point consideration has been given only to will again be no relative advantage by virtue of the D.„.,. the "savings" of delay, ,^S, within the subnetwork for those and D,i,,<. considerations on the south leg of r. same vehicles predicted to receive service at intersection q Hence, the delay consequences of both the cases described (east-west legs) during the alternatives available at q (0. may be expressed as ^iilK.w). hy comparing the delay experienced downstream (D.„...'.V - D.,..,o) = (D„..,.'^. - D.,„.») = 0 (E-37) at the neighboring intersections. An attempt is next made to define the expression for the which is based on the assumption of uniform deceleration relative delay*, ,,D, caused within the subnetwork, in terms and acceleration characteristics (refer to Eqs. D-14 and of the previously defined delay at q, Dru and Oj.^- (isolated D-I5). case, see Eq. D-9), and the relative delay accrued to the The next step is to estimate the number of vehicles of the vehicles at the neighboring intersections which are predicted total considered, q,r.4''(jc,y), that must decelerate (and to be released from the (opposite) north and south legs accelerate) due to the formation of a queue on the south of q. leg of r (or in the case of the first vehicle, the .(^mx.s Here, the predicted consequences of the two alternative phase) during the two alternatives. actions at intersection q must again be compared, as fol• Referring to Eq. E-22, it will be recalled that ^K"'At lows: represents the interval of time measured from the first 1. Terminate current phase, initiate ..^(jix s now, or arrival until the dissipation of the queue. Since arrivals at 2. Defer action 1 by the extension nAt of „(: mw r are assumed to take place over ^WAf (see Eq. E-16), referenced from the same event, the following conditional First, the delay caused within the subnetwork is expressed, relationships may be written: as follows: If "M^p = «it^p' + „Dr|x,s (E-44) K"' ^ M° (E-38) where, from Appendix D, the queue persists during the entire time of the n rA°ix,y) (E-45) arrivals. Hence, and n^,^p- = „Af(,_ _.£, + p + _^ + (£-46) ^>X"'^''j^ (E-39) As previously, the first pre-subscript indicates the intersec• and tion to which the deci.sion is applied and the second indi• cates the particular intersection at which the relative delay (E-40) is considered. t\ 1=1 / f The next choice is to investigate a particular intersection However, if —namely, r—within the subnetwork q, r, s, t, u. (E-41) • Although this term is denoted as "relative delay," it should be noted only a portion of the ^^^A'>(.x,y) vehicles considered in the that Its sign may be positive or negative If it is negative, vehicle-seconds are predicted to be saved within the subnetwork by the north-south depar• general delay equation incur the delay, as follows: tures if deferred an additional nM seconds. 48 DELAY IN QUEUE ^GlN.S + (<^A|N,S ~ 'f> AiN.s) (E-51) At By referring to Eq. E-10, the relative delay in queue at r is written as and the following conditional expressions may be written: If - ,.r(£>««^' - />/A,E,W)S^^ (E-47) (E-52) where then , rDjSjj g"^* — delay suffered within the queue on the south leg of r to those vehicles released r« iS ' r«i8 (E-53) from the north-south legs of intersection However, if q if the current phase, q<^GiE,w> is / > Af^A -I- p (E-54) tended by nAt; and q.rJDgSN s^AiK.w = delay suffered within the queue on the then south leg of r to the vehicles released r«'is = 0 (E-55) from the north-south legs of intersection q if the current phase, q<^GiE,w>termi• Substitution of average values for the estimates in Eq. E-50 nated immediately (i.e., m^AAt = predicted interval of time necessary to serve vehicles originally queued on the south leg of r, referenced from the instant that the first vehicle (5',-5,) Arj^- arriving from intersection q (as a result of the m*\+P /r- I immediate phase change), joins the existing queue at r, until this queue is served. j=i+j8 r VL t=i+i8 Ar, Since r^ig^A is defined as the number of vehicles in queue (E-48) on the south leg of intersection r at the time of the first arrival from intersection q (resulting from the aforemen• in which the summation limits reflect that the delay to the tioned decision at q), the following relationship may be vehicles are considered later in time than Eq. E-U, as written: defined by: »l*A+i8 ^At = interval of time which is estimated to elapse be• (E-57) tween the first arrival on the south leg of r, due to i=i+/3 the extension of the current phase at q, and the first Substitution of average values for the estimates and solu• arrival from the opposite pair of legs at q, due to tion for m Hence, by making reference to the discussion immediately (E-58) r^isAf preceding Eq. E-32, the following may be written: jSAf = <^AiE,w — I difference in travel time | (E-49) Similarly, one may solve for r^siN.s'**' and r^alN.s"** in order to choose /iCgiN.s'^A- Because these estimates are The following restrictions and definitions apply to Eq. defined (following Eq. E-20) for the case to the 0th power E-48. east-west departures from q, the results are simply stated The arrivals at r, a'j, considered in Eq. E-48 should re• in terms of average values, as follows: flect only those contributions from the north-south legs of the newly initiated qG1N,S phase is deferred 49 by an additional nAt seconds, may now be expressed as Similarly, for the alternative of releasing the vehicles from the legs currently receiving the red phase as soon as possi• ble (after then j=l+'> r (L i=l+y ^ -i / S (E-61) ,..HD,I..C*A = 1*^1 y SAtA (E-74) Inasmuch as the restrictions and definitions of terms used in Eq. E-61 are analogous to the preceding, the details are and excluded and only the results are given, as follows: r\ i=l+/3 /S y==P+ n (E-62) (E-63) However, if (E-76) r\ i-lr^ /s (Inasmuch as the same number of arrivals, r^i*A(z), is considered in each instance (<^A OT nAt), it was assumed then in Eq. E-63 that the duration of the deferred q<^GlN,s phase is at least as long as the one considered in Eq. E-Sl with equivalent departure characteristics; if this is not the case, I-1+/3 /s Eq. E-63 would be modified to reflect the same number of and departures over a shorter or longer period.) ,,,D„..,.0A= [K, X «.A'.) (E-78) (E-64) (E-65) GENERALIZING EQUATIONS ,(,a-d)sAt Although the particular equations were only developed for riVis"-^^ + ,a,s'n«^'^t (E-66) intersection r of the subnetwork, the extensions of these equations to s, t and u are obvious and were assumed with• out further explicit presentation. Further, in order to more DECELERATION AND ACCELERATION TERMS readily develop the concepts, a particular initial condition was chosen (i.e., state of signal display at q, ,I<^G|E,\V, One may now write the delay to those vehicles of the total q<^R|N,s)- Because a number of possible signal states exist considered, ,,,/i^A(z), that must decelerate (accelerate) at an intersection, the following discussion and Table E-1 due to conditions at r, in an analogous fashion to that ex• pressed in Eqs. E-38 to E-43. Therefore, if have been included for purposes of clarification and re• view. In Table E-1, Col. 1 specifies the particular pair of (E-67) legs at q for each possible signal state; Col. 2 gives the then signal displayed to each of the two pairs of legs at inter• section q; Cols. 3 and 4 show that the "savings" equation (E-68) (as expressed for the neighboring intersection r) previ• r\ i=l+T /S ously developed (refer to Eq. E-3), applies to the vehicles on the north and south legs for signal state I and to the and vehicles on the east and west legs for signal display II; ,„n4 l+T V Col. 5 indicates the total number and source of the vehicles (E-69) ( to be considered in the calculation of Cols. 3 and 4 (that is, in case I the vehicles predicted to incur relative savings at However, if r are departures from the south leg of q over period nAt (E-70) that choose a northbound (straight through) direction, whereas in case II left- and right-turning movements are then contributions as indicated); Cols. 6 and 7 show that the delay equations (as expressed for the neighboring intersection r) (E-71) previously developed (refer to Eq. E-47 for delay in 1=1+7 / S queue) apply to the vehicles on the east and west legs for and case I and the north and south legs for case II; and Col. 8 gives the total number of vehicles and their source which K, X «.Af.) (E-72) are considered in the calculations of Cols. 6 and 7. i=l+T / S 50 TABLE E-1 APPLICATION OF DERIVED EQUATIONS TO VARIOUS SIGNAL STATES AT q LEG SIGNAL SIGNAL D» "^t^Aoix, y, z) ^£)«At ,A'^(x, y,z) (PAIR) STATE AT q STATE (i) (4) (5) (6) (7) («) (/) (2) rA*^ixy^.,yE) = I E, W qll|E,W n B Xal^'S^tsAfJ X'i{(^>w^.wA'v) + 1=1 1=1 N,S q<^GlX,S "'^'^"{xy^ys) = r^*UZs) = II E,W In. w 11<#>G|E,W n B Xit^^'W^twAf,) 2u{(z.s^.sAf.)} 1=1 1=1 N,S qUlN,S + (y.E^.EAf,)} III E, W qnlE.W No calculation is performed, as an amber display indicates transition period. Further, it is anticipated that the computer need not interrogate the signal until N,S q<^AlX.S the predetermined q<^Glx.Sn,in elapsed. IV E, W q<#>AlE,'\V No calculation is performed, as an amber display indicates transition period. Further, it is anticipated that the computer need not interrogate the signal until N,S ilUl.N.S the predetermined (I DECISION FUNCTION NOMENCLATURE AND DEFINITIONS One must now consider the basis for choosing a particular q,r,s,t,u = the intersections that are considered to action from the alternatives available. A function, „(")„At' form the subnetwork, where the de• may be developed which expresses the difference in relative cision with respect to traffic signal dis• delays and savings within a subnetwork for the two as• play is to apply to q; sumed alternatives at intersection q. ii<^G|E,w. qitix.s = the phase at intersection q which dis• In terms of previously defined notation, the following plays the green signal to the east-west equation is introduced: legs and the red to the north-south legs, respectively; q0„Af -= qW„A, + "^'q^' " "^'q^' (E-79) 0«At = quantity employed in the case of the or isolated intersection, in order to test for q0«.u= "^'q{(q-S-qD) + (^-,D)+ • • • („5-„D)} minimum delay between the alterna• (E-80) tives of an immediate change in signal The computer will perform the following test: phase or a postponement of nAt; If n = integral number of units of time, Af, considered for the proposed extension qWA^^O (E-81) of the current phase; extend the current phase, because more or equal delay is = relative savings to the east-west traffic predicted to be accrued by terminating the current phase. in the case of the isolated intersection; However, if relative savings within the subnetwork, „0A, < 0 (E-82) for the considered nA/ extension of the current phase at intersection q, exclud• less delay would be incurred by changing the phase now ing the savings accrued at q; than At from now. However, it may be necessary to calculate ,,W.JA/. ,|WIA(. • • q^nAf because less delay may «Af s "^^ S nAt . C nM C . be incurred at these other times. It should be noted that q,t''> q.ii"* the contributions to "^',^S' which repre• if any of the subsequent ,,(")'s are positive the procedure sent the relative savings at each of the may terminate and the particular extension whose W yields intersections neighboring q, to those a positive quantity is accepted. vehicles released from q (during the 51 alternatives) and seeking service at r, s, the vehicles considered are arrivals t, and u, respectively; from q during the current green ex• tension; "^'q.r^s" = the delay accrued on the south leg of M" — predicted integral number of time units. intersection r to those vehicles released At, over which departures from q ar• from the east-west legs of intersection rive at r. The superscript signifies that q and seeking service at r, for the al• the vehicles considered are arrivals ternatives of the immediate change of from q during the proposed (green) phase and extension nAt, respectively extension; (assuming current phase at q is ,,<^GIE,W. <^uiN,s); = A-\-B= time average of A and B over specific "^'yS — relative savings within entire sub• interval of time; network; = predicted integral number of time units. "^',D = relative delay within entire subnetwork; At, referenced from the time of the first qJfiE. r^iw. B^is = estimates during the interval of the arrival to the south leg of r, until the proportion of left turns from the east queue on this leg is dissipated. The leg of intersection q, right turns from superscript 0 indicates that the vehicles the west leg of intersection r, and are those arriving from the legs at q straight-throughs from the south leg of which receive the proposed (green) intersection s, respectively; phase extension (east-west legs of q); '*^',,,,/4''(x,y,z) = prediction of the number of arrivals at • '^"'siE.w = predicted integral number of time units. r resulting from the extension nAt of At, referenced from the time of the first the current signal phase at q (i.e., arrival to the south leg of r, during q<#>(;lE,w)'> which the last vehicle being considered S,,{/t 4-B},= = i,.,A,= + '4,.,B.r from the east-west (green) extension at q is serviced at r; ^ nM n ".if D script signifies that the arrivals con• "•^'q.tO, "^'ii.u^ = the contributions to "\D' which repre• sidered are from q during the next sent the relative delays at each of the green phase, if begun immediately intersections neighboring q, to those ve• (<^G|x,s); hicles released from q (during the al• prediction of the length of queue (num• ternatives) and seeking service at r, s, t, ber of vehicles) on the south leg of and u, respectively; intersection r at the time of the first arrival from q (north-south legs) dur• q liJas'**!'' ^ = the delay accrued within the queue on ing the new green phase if initiated the south leg of intersection r to those immediately; vehicles released from the north-south legs of q and seeking service at r; for I'^slx.s''' A = similar to the definitions given for the the alternatives of releasing the vehicles respective notation with the 0 super• after the proposed red extension or scripts; however, the superscript terminating current phase and releasing signifies that these terms apply to the the vehicles after the amber phase, re• vehicles released from the opposite legs spectively; (north-south) during the proposed |3 = predicted integral number of time units. green phase, which is initiated im• At, between the time of the first arrival mediately; on the south leg of r, which would have resulted by extending the current phase i^^six.s"^', at q, and the first arrival from the op• rK^"^'" = similar to the definitions given for the posite pair (north-south) of legs result• ing from the decision to change the respective notation with the 0 super• signal phase immediately; scripts; however, the nAt superscript = predicted integral number of time units. signifies that these terms apply to the At, over which departures from q arrive vehicles released from the opposite legs at r. The superscript signifies that the (north-south) during the proposed vehicles considered depart during the green phase which would be initiated proposed next green phase which would following the extension by nAt of the be initiated if the decision was to current phase; terminate the current phase immedi• y = predicted integral number of time units. ately; At, between the time of the first arrival B = predicted integral number of time units. on the south leg of r, which would have At, of the duration of the new green resulted by extending the current phase phase (as displayed to north-south at q, and the first arrival from the op• legs); posite pair (north-south) of legs result• m'K = predicted integral number of time units. ing from the same decision to extend At, which are necessary to serve the the current phase by nAt (deferred vehicles originally queued at r, mea• <^(jlN-,s); and sured from the instant that the first ii®iiM ~ a quantity employed, in the case of the vehicle arriving from intersection q subnetwork defined by the intersection joins the existing queue at r until the q, to test for minimum delay between existing queue is served. The super- the alternatives at intersection q. APPENDIX F CRITERIA FOR SELECTION OF THE DIGITAL COMPUTER A phase of the current research project is to determine mining the requirements necessary to achieve this objective the speed and size of digital computer(s) to be used in of creating an adaptive control system, and also describes implementing the developed system of equations in real the computing systems currently available that will ac• time. This appendix describes the method used in deter• complish these goals. 53 FORMAT OF INPUT DATA FROM SENSORS detectors 2 and 4, depending on the state of the signal (e.g., green N-S, detectors 1 and 3 operating; or green As described in Appendix C, the data coming from each E-W, detectors 2 and 4 operating). Figure F-2 shows the intersection are grouped into 14 bits of information relat• arrangement of detectors at a general intersection. ing the status of each detector or sensor and the current Bits 8, 10, 12, and 14 give the condition of detectors signal state at the intersection. Also, the intersection num• 5, 6, 7, and 8, respectively. Bits 15 through 21 give the ber is generated to help detect channel-skipping errors that current intersection number of the data being displayed. would result in putting the data out of synchronism. The (The seven bits allow for 128 intersections.) input data folrmat is shown in Figure F-1. Bits 1, 2, 3 give the current state of the signal, the FORMAT OF OUTPUT DATA TO INTERSECTION various signal states being as given in Table F-1. Bits 4 and CONTROL SIGNAL 6 give the state of stop-line detectors 1 and 3 or stop-line When the computer program decides that a particular • D„ D„ D„ . D , represent the possible 8 detectors located at an intersection. intersection should change the state of the signal, an output word consisting of 9 bits is generated. Figure F-3 shows the output bit configuration. When bit 1 contains a 1, the TABLE F-1 hold circuit switches the signal from local control to com• puter control, or vice versa. When bit 2 contains a 1, the SIGNAL STATES AND CODING actuate circuit changes the signal state. Bits 3 through 9 CODING contain the number identifying the intersection that is to be changed. OCTAL SIGNAL STATE EQUIVALENT N,S E,W OF BINARY BINARY BIT DATA INPUT RATE R G 101 A sampling rate of 60 samples per second is necessary, R Y 001 due to considerations of multilane coverage with a single G R 010 loop detector as discussed in Appendix B. Y R 000 To determine the presence of a car at any approach I 2 3 >( 5 6 7 8 9 10 II 12 13 14 15 16 17 18 19 20 21 • 0 0 0 0 0 "I'Oa "5 "6 "7 l'8 ^ SIGNAL OR OR INTERSECTION NUMBER CONDITION Dj Figure F-1. Input data format. • 3 ^ 5 6 7 8 9 T HOLD INTERSECTION • ACTUATE NO. E Figure F-3. Output data format. detector there must be a 0 from the previous detector reading and a 1 from the present detector reading. That is, a search must be made for a 01 combination at any detector 5 through 8 over a previous and present data reading. To determine the departure of a vehicle at the stop-line detector, there must be a 1 from the previous detector • reading and a 0 from the present detector reading. Figure F-2. Typical detector locations at an intersection. When the approaching or departing vehicle is sensed by 54 a detector, an appropriate storage location is updated by list of instructions that will then transfer to the appropriate the computer. This technique yields a current vehicle coding to update the vehicle counts. To illustrate further, count to be employed in the programmed calculations. this transferring technique is analogous to the "computed GO TO" statement in FORTRAN; i.e., for the 256 com• DETECTOR DATA ENTRY INTO COMPUTER binations the FORTRAN statement appears as The data from the detectors are presented to the computer GO TO (1,2, 3, ,255, 256), IR in a sequential mode; that is, fully multiplexed (as de• where IR contains the sum produced by shifting and scribed in Appendix C) through an I/O data channel. adding the previous and present data together. By shifting and adding the previous data to the present DECODING METHOD USED IN COMPUTER data the presence of a car can be determined at any one, The data word is read into the computer through an I/O all, or any combination of the four approach detectors channel. Then the intersection number is extracted from (D5 to D8) immediately. Of the 256 combinations possible this data word and placed into an index register, which from the eight bits containing the approach detector infor• allows for data to be stored in the proper place of the data mation, 175 yield an indication of at least one car present. set array. Masking out all but bits 7 through 14 of the data The possible detector combinations, together with the word leaves the bits for approach detectors 5 through 8. decimal equivalent of the binary coded (8-bit) word that Now, the previously stored bits for this intersection are will produce these combinations, are given in Table F-2. shifted left one place, the present data are added, and the The transfer list contains 256 values, each of which rep• sum is placed in an index register. This index register can resents the appropriate location to update the vehicle be used to transfer control to a particular location in a counters that these detectors have indicated. To illustrate the method of decoding, the previous set of data is assumed to contain all O's and the present set of data to contain all I's. Then the bit configuration when combined will be as shown in Figure F-4. When these »5 data are loaded into an index register and transferred to 10 [oTT the combination list, they will go to location 125 octal or Figure F-4. Bit configuration for a 85 decimal and update the vehicle counts of all four vehicle presence at each detector. detectors. To decode the two stop-line detectors a similar approach was taken using only 4 bits of data, giving 16 possible com• bination sets. Also, a similar transfer list is set up. TABLE F-2 CODED COMBINATION OF DETECTORS TIMING REQUIREMENTS POSSIBLE DECIMAL EQUIVALENT OF In a worst-case analysis of the foregoing data decoding DETECTOR BINARY CODED (8-BIT) scheme—that is, where a car is detected at each detector COMBINATION WORD simultaneously—it required 76 computer cycles (5) per D8 1, 9, 13, 33, 41, 45, 49, 58, 61, 129, 137, 141, intersection to decode, based on programming the research 161, 169, 173, 177, 185, 189, 193, 201, 205, agency's current computing system. 225, 233, 237, 241,249, 253 Based on the proposed 60-samples-per-second scanning D7 4, 6, 7, 36, 38, 39, 52, 54, 55, 132, 134, 135, 164, 166, 167, 180, 182, 183, 196, 198, 199, rate, 16.67 millisec are available to decode 116 intersec• 228,230, 231,244, 246, 247 tions, or 143.6781 |ixsec per intersection. Therefore, the D6 16, 18, 19, 24, 26, 27, 28, 30, 31, 144, 146, time per computer cycle is 143.6781/76 = 1.89 ^usec/cycle, 147, 152, 154, 155, 156, 158, 159, 208, 210, and the computer must have a cycle speed greater than 211,216,218,219, 220, 222, 223 1.89/.sec. D5 64, 66, 67, 72, 74, 75, 76, 78, 79, 86, 98, 99, 104, 106, 107, 108, 110, 111, 112, 114, 115, 120, 122, 123, 124, 126, 127 STORAGE REQUIREMENTS D7, D8 5, 37, 53, 133, 165, 181, 197, 229, 245 D6, D8 17, 25, 29, 145, 153, 157, 209, 217, 221 The analysis has shown that 2,011 storage locations will D6, D7 20, 22, 23, 148, 150, 151, 212, 214, 215 be needed, allocated as follows: D6, D7, D8 21, 149,213 Previous D5-D8 detector data 116 D5, D8 65, 73, 77,97, 105, 109, 113, 121, 125 Previous D1-D3 detector data 116 D5, D7 68, 70, 71, 100, 102 103, 116, 118, 119 Previous D2-D4 detector data 116 D5, D7, D8 69, 101, 117 Vehicle counts at each detector 928 D5, D6 80, 82, 83,88,90,91,92, 94, 95 Computer program (approx.) 400 D5, D6, D8 81, 89, 93 Contingency and/or expansion 335 D5, D6, D7 84, 86, 87 85 D5, D6, D7, D8 Total 2,011 55 SUMMARY OF DATA ACQUISITION REQUIREMENT qON, = „,„D,Af+ . . . +q,uDiAj (F-2) From the foregoing analysis, it is found that the computer 7. Calculate 0,^?, which is the total "savings," qS^j, must have the following requirements: minus the total "delay caused," „DN,. 8. If 0,Af is positive (or zero), extend current signal 1. A cycle speed greater than 1.89 microseconds. state by j'Af and proceed to intersection q -f 1. 2. A minimum core storage of 2,000 words (each 9. However, if 0,^, is negative, and / < K, where K word should have 18 bits). will be the stored upper limit (an integer), increment / to 3. Address modification capability (i.e., index registers i + 1 and return to step 5; when i = K, go to step 10. or general registers). 10. Choose least negative from computed 0's (e.g., 4. A high-speed data channel (125,000 words/sec f")iAf. WjAf. and 0.)^,, where K = 3), calling this optimum transfer rate). value 0,.A(. 11. Signal should be changed in i'Af seconds. Proceed GENERAL FLOW FOR IMPLEMENTATION OF to next intersection, q + 1. MINIMUM-DEUY CRITERION Appendices D, E, and G define the "saving" and "delay" METHOD OF EVALUATING REQUIREMENTS equations as they apply to a given intersection. For imple• mentation of these equations the general flow chart in From an analysis of the equations to be programmed for a Figure F-5 was constructed. digital computer (Appendices D, E, G) it was found that Generally, the sequence of operations performed by the the "savings" equations contained three basic expressions; digital computer is as follows: that is, 1. The estimated delay saved by those vehicles serviced 1. Determine current state of signal at intersection q. (from the two legs) during A?, which otherwise would Possible states for symmetrical display are as follows: have to suffer the amber, red, and lost time resulting from E,W N,S an immediate change in phase (see Eq. G-41). 2. The delay saved which accrues to those vehicles qGlE,W which are served earlier in time, as a result of the previous q<^K[K,W il<^GlN.S departures (see Eqs. G-44 and G-45). a<^R|n,w fl<#>AlN,S 3. The additional relative saving within the subnetwork, (1<#>A1I0,W expressed as the sum of the individual savings at each of 2. If the total elapsed green time (i.e., „<^OIE.W> ^n^*" the neighboring signalized intersections (see Eqs. G-55, sured in seconds from the instant the phase changes to G-56, and G-60). n<#'oiK,w; assuming that is the current signal state) is less The "delay" equations contained only those equations than or equal to the minimum green time (i.e., q(}'To.w„,i,i' expressed by item 3 (compare Eqs. E-11 and E-48). stored for (possibly) each approach leg for each inter• The equations described in the foregoing were pro• section) proceed to intersection q + 1. If not (i.e., greater grammed in FORTRAN IV* (9, 10) after some simplify• than), go to step 3. ing assumptions were applied. These assumptions were 3. Test to determine if a vehicle (i.e., on either leg) has made to expedite the preliminary programming analysis. been waiting during the red phase, „(/)uix,s- ^ yes, deter• The major assumptions were as follows: mine the time of arrival of the vehicle, .((^"uix s. measured 1. Certain predictor models that are updated use multi• in seconds from the time base of the change of signal to variate linear regression techniques and other predictor (i<^ulx.s- Subtract this arrival time, „<^"I{|X.H, from the models use simple linear regression techniques. It was elapsed red time, qK^mx.s- If greater than the predeter• assumed here that all predictor models would use the mined (fixed storage) <^K ,„,,^, change the signal phase and simple linear regression technique. proceed to intersection q-f 1. If not (i.e., less than or 2. In some cases particular upstream intersections (or equal to), go to step 4. sources) are not signalized. Hence, measurements would 4. Each intersection, q, to be evaluated is assumed to not be available for predicting arrivals at the intersection be a member of a subnetwork of intersections of (at least in question by the proposed predictor models. Therefore, one and) no more than five (q, r, s, t, and u). another model must be used. It was assumed that the 5. Compute the total savings, .li'x (in vehicle-seconds) proposed model has the same storage and time require• for the particular subnetwork defined by intersection q, ments as the model used when the source conditions are based on the alternatives at q (i.e., change signal state im• not satisfied. mediately, or in lAf, or 2At, . . ., or X:Af), where 3. Upper limits were applied to the number of storage locations allocated for the measured and predicted de• parture rates for each stop line. The departures for that and the terms on the right side of the equation represent portion of the green phase which extends beyond these the "savings" at intersections q, r, s, t, and u, respectively, limits were assumed to be calculated from previous results based on the alternative (i.e., now or in iAt, where /= 1, and this information would be retrieved as required. 2, . . ., K) then go to step 6. 6. Similar to step 5 above, with "savings" changed to * FORTRAN IV is a problem-oriented automatic coding system designed primarily for scientific and engineering computations, and closely resembles "delay caused" and the equation changed as follows: the ordinary language of mathematics. 56 DETERMINE CURRENT STATE OF INTERSECTION 0 WHICH WE ARE EVALUATING PROCEED TO NEXT INTERSECTION W/OUT CHANGE CHANGE 0 SIGNAL PHASE IMMEDIATELY AND PROCEED TO SUBNETWORK \ (J) NEXT MATRIX FOR INTERSECTION GIVEN INTERSECTION (' COMPUTE N ^ C ' COMPUTE \ EXTEND CURRENT ^ 0 SIGNAL STATE By I At GO TO NEXT INTERSECTION K > 0 COMPARE 0 SELECT LEAST NEGATIVE I CHANGE SIGNAL 0 STATE AT Figure F-5. General flow chart of saving and delay equation criterion. 57 4. Although the equations containing the arrival rates (a) Perform 900,000 cycles in 2 sec (i.e., have a were written in terms of A*, the arrivals were measured and computer cycle time of not more than 2.2 /xsec). predicted over periods of 2A/. (b) Have floating point capabilities (software or hardware). Then, using 10 cycles (10) for a multiplication and (c) Have address modification features (i.e., index 18 cycles {10) for a division, the total number of cycles registers or general registers). necessary was computed for each equation, with the (d) Have a minimum of 37,000 words of core following results: storage. Ti, equation Type 1, 155 cycles (e) Have a data channel. T2, equation Type 2, 565 cycles (f) Have a real-time clock. J3, equation Type 3, 822 cycles 2. For the data accumulation scheme, a computer should: The 116 signalized intersections in White Plains, N. Y., (a) Perform 76 cycles in 143.6781 /zsec (i.e., have used as the typical city, were categorized into five different a computer cycle time of not more than types of intersections. Table F-3 gives the types of inter• 1.89|iisec). sections with the number of each type and the number of (b) Contain a minimum of 2,000 words of core the saving and delay equations necessary at each inter• storage (18-bit words). section type, as well as the required number of computer (c) Have address modification features (e.g., index cycles. The analysis shows that the total computational registers or general registers). scheme will require 879,216 cycles, or approximately (d) Have a high-speed data channel. 900,000 cycles. Also, the storage requirements for the data that will COMPUTER SYSTEMS AVAIUBLE have to be stored during the calculations (e.g., measured departures, predicted departures, measured arrivals, pre• On examining the prerequisites, it is seen that at least two dicted arrivals, queue lengths, length of the signal phases possible routes are available. One method is to acquire for each intersection), were estimated to be approximately two machines, each performing in parallel one set of the 30,000 words of core plus 20 percent for contingencies and requirements (i.e., data acquisition and delay computa• program instructions. Thus, approximately 37,000 words tions). Another method is to acquire one machine that of core storage are needed. can perform all requirements (i.e., both sets) sequentially in the specified time limit (2 sec). TIMING REQUIREMENTS Table F-4 details components and costs for a single- processor computing system, called System A, that will be From the foregoing analysis, the total calculations must be able to fulfill all of the requirements within the specified done in At, which has been established as 2 sec. Therefore, time limits. This system will allow overlapping of the data 900,000 cycles must be run in 2 sec, or 2.22 ^isec per cycle. gathering and computation functions, thus allowing the disk storage to serve as an extension of core storage. This SUMMARY OF COMBINED REQUIREMENTS is necessary because only 32,000 words are available and almost 39,000 are required. The analysis has given the following requirements to Table F-5 details components and costs for a two- achieve'the projected data rate and computational schemes: processor computing system, called System B, that will be 1. For the computational scheme, a computer should: able to fulfill all of the requirements if the data gathering TABLE F-3 ANALYSIS OF SIGNALIZED INTERSECTIONS OF TYPICAL CITY " BY TYPE, DISTRIBUTION, AND COMPUTER CYCLES REQUIRED EQUATIONS REQUIRED NO. IN TOTAL CYCLES (TYPE AND NO.) INTERSECTION TYPICAL -REQUIRED FOR TYPE " CITY* SAVING COMPUTATION " 1. q, r, s, t, u 1 Ti 4- T. -1- 8T3 IOT3 15,516 2. q, r, s, t 21 Ti -f- T. -1- 6Ta 8T3 256,788 3. q. r,s 38 T, -1- T= -1- 4T3 6T3 339,720 4. q,r 41 Ti -H T= -1- 2T3 4T3 231,732 5. q only 15 T, 4-T2 2T, 35,460 All 116 879,216 White Plains, N.Y. •> See Figure E-2. °'^i = 155 cycles; Tj = 565 cycles; =: 822 cycles. 58 TABLE F-4 TABLE F-5 COST ANALYSIS FOR A SINGLE-PROCESSOR COST ANALYSIS FOR A TWO-PROCESSOR COMPUTING SYSTEM, SYSTEM A COMPUTING SYSTEM, SYSTEM B COST ($) COST ($) MONTHLY MONTHLY MONTHLY MAINTENANCE MONTHLY MAINTENANCE COMPONENT RENTAL PURCHASE FOR PURCHASE COMPONENT RENTAL PURCHASE FOR PURCHASE Hardware: Hardware: 1 Processing unit with: 6,265.00 257,700.00 250.00 1 Central processor with: 2,050.00 73,800.00 250.00 1-nXc cycle time/ 2-;4sec cycle time 4 bytes' 4,096 words of core 131,672 bytes of core memory (18 bits) storage 8 I/O channels 16 general registers 8 index registers 63 instructions 78 instructions consol-printing-key- interval timer board 6-line/in. pin• 1 Intercomputer coupler 600.00 24.000.00 60.00 59.25" feed platen 1 Central processor with: 2,300.00 82,800.00 265.00 channel attachment 2-/isec cycle time integrated single-disk integrated console with storage drive, keyboard and printer 272,000 woids 4,096 words of core interval timer memory (18 bits) 1 External interrupt 30.00 1,260.00 1.00 8 I/O channels 1 Floating point arith• 275.00 11,550.00 11.00 8 index registers metic (44 additional 78 instructions instructions) interval timer 1 High-speed (250 nsec ') 700.00 29,400.00 28.00 9 Additional 4,000 in• 3,150.00 113,400.00 360.00 general registers crements of core 1 High-speed 650.00 27,300.00 29.25 memory (500,000 bps") 1 I/O equipment adapter 100.00 4,000.00 15.00 multiplexor channel 1 I/O equipment 1,450.00 58,000.00 295.00 1 Low-speed 350.00 14,680.00 17.75 400-cpm, 80-col card (200,000 bps ") reader multiplexor channel 400-line/min printer (for card reader- 200-cpm, 80-col card punch, and printer, punch etc.) 1 Code image read 25.00 1,000.00 35.00 1 Card reader punch, 525.00 26,250.00 75.50 (binary read) read 400 cpm, 1 Code image punch 25.00 1,000.00 35.00 punch 120 cpm (binary punch) 1 Printer, 875.00 44,275.00 87.50 Total 9,700.0 358,000.00 1,315.00 240 lines per minute 120 print positions Software: Total 9,670.00 412,424.25 500.00 FORTRAN IV compiler—load and go type, no object code produced; therefore, must recompile each time program is to Software: run. Disk resident monitor with I/O capabilities Assembler—"ART" (assembler for real time). Disk resident assembler Utility package, input-output routines. Disk resident FORTRAN IV compiler and library Library of scientific routines. Disk resident utilities and loader Floating point arithmetic. Scientific subroutine package (more than 130 FORTRAN sub• Executive or monitor routine. routines) » Byte = 8 bits, This item for purcliase only <• nsec — nanosecond (10-» sec). bps = bytes per second. ( rate is relaxed to 56 samples per second (instead of 60 will cost the same—approximately $455,000, or $6,740 samples per second). per month. In addition, a relatively small area must be The cost analyses in Tables F-4 and F-5 indicate that secured and air conditioned (approximately 10 tons) to both systems rent for about the same ($9,700 per month) house the computing equipment. The costs associated with or on a purchase-maintenance/month cost System A will this section of the installation have not been included in be $412,424.25-$500, and System B will be $358,000- the estimated rental, purchase-maintenance costs. $1,315. Extrapolating over a 5V^-year period both systems The programming time required for a program as com- 59 plex as intersection control will require V2 to 1 man-year ADDITIONAL UTILIZATION OF COMPUTING SYSTEM to write and debug. The major part of the programming Aside from doing the traffic controlling, the computer effort will be in FORTRAN; but although FORTRAN can system can be applied to the municipal government's com• convert an algebraic-type statement into a machine lan• mercial data processing requirements. This can be done guage code, there are times when conversions do not take during a part of the day when the traffic is light and the advantage of special features of the particular machine or local controllers will suffice, or during the late evening it adds redundant code to achieve generality at a sacrifice hours. of computing speed. Therefore, certain portions of the The computer may be employed as a tool in the post- program should be written in a machine language code to analysis of traffic data, as collected throughout the control achieve the efficiency necessary to a program that will run periods or at other specified times, in order to improve its literally thousands of times per hour. The total cost for control function. It may also be used in the performance this programming effort will be approximately $25,000. of accident studies, etc. APPENDIX G IMPLEMENTATION AND PREDICTION TECHNIQUES AS APPLIED TO THE SUBNETWORK EQUATIONS In order to apply the philosophy as developed in Appen• turning movement. Such a prediction would best be made dices D and E, a number of quantities must be predicted. by including all quantities which are known to be cor• The predictors and the models employed will indeed de• related with the flow rate and the most recent measure• termine the sensitivity of the network's signal response to ments obtained by the system. It should be noted that not the fluctuating traffic demands. Hence, the merit of the all of the necessary predictions to be made are as critical proposed (implemented) control system will obviously rely or as fluctuating as the foregoing example. on the judicious selection of the aforementioned prediction The variances on the traffic quantities are believed to be techniques. attributed to both attainable and unattainable (i.e., to the One of the problems that plagues even the most ad• system's instruments) complex factors. For example, de• vanced traffic signal system known to be operational is its parture rates at a particular leg of an intersection may be reliance on certain expected values. These averages, which affected by time of day, day of week, season, weather, turn• are used as predictions, of important traffic quantities may ing movements, actual delay experienced in the network, have the added flexibility of being varied as a function of length of queues, special local events, international news, time (clock), season (calendar), observations (human), personal and emotional experiences, etc., some of which etc. However, these predictions are generally based solely may be correlated with each other. Based on the foregoing on past measurements which were observed during the last discussion and the traffic data analyzed, it is believed that hour, day, or year. Further, the measurements may be the system proposed should lend itself to updating tech• taken at other than the particular intersection or locale to niques in order to include the most recent information, which they are applied. Such a philosophy might be ac• when necessary. Hence, as the computer continues to ceptable for a freeway or highway where the statistics at interrogate the remote instrumentation (i.e., to sample the various points may be assumed invariant as a function of dynamic network), the predictions would be revised to location. However, applying this approach to urban traffic reflect this additional information. In this manner an at• predictands could lead to poor control. tempt will be made to make the system respond to both It is the very nature of the traffic characteristics experi• sudden changes in conditions (affecting the predictions) enced in urban areas to include large variations in the and the more subtle variations which occur throughout the important quantities (i.e., necessary for effective, real-time day. control) which cannot be forecasted with "yesterday's" Although it is not the purpose of the current study to observations. These wide fluctuations occur not only from empirically validate various prediction models, such a day to day, or hour to hour, but also within seconds. For study would be necessary for the successful implementa• example, consider a stop line at the north leg of a hypo• tion of the control system, and should be performed (in thetical intersection; departures have been flowing at the part) before the system is operational. In view of this saturation rate since the end of the starting transient. limitation, a few theoretical prediction methods which Suddenly, a vehicle desires to turn left, but must wait for a appeared to be reasonable in their applicability to the de• gap in the conflicting traffic; in a matter of seconds the veloped equations were investigated, and the empirical flow could be reduced to zero vehicles per second. One validation of other research work in this area was relied problem suggested by this example is that of obtaining a upon. "good" prediction of the departure flow subsequent to the In selecting the prediction models the computational re- 60 quirements of the digital computer were considered, be• Setting the partial derivatives of Eq. G-3 equal to zero cause the predictand is most valuable if it can be computed gives simply and quickly so as to be applied within the real-time limitations. Also, this appendix makes "reasonable" sim• plifying assumptions, for the purpose of further reducing Oa the computational requirements imposed on the machine -~{2„(j'.-a-y3iJrH- . . . - fi,nX,„i)-] = 0\ by the minimum-delay equations as presented in Appen• dices D and E. It is believed that good predictions of the necessary traffic quantities (i.e., those with small possible errors) may be obtained by combining simple linear regression, P;^{'^w(yi-a~l3,x,,- •PmX..ny}=0 OPm multiple linear regression, and average values, with a (G-4) weighted moving average technique. The complexity of the particular model proposed for each of the quantities to be whose solutions will yield the sought for estimates, a, predicted will depend in part on the apparent physical ^1 Pin- reasonableness of the assumptions, the prediction interval required (confidence level), and the instrumentation as GENERAL EQUATIONS FOR ESTIMATES OF a AND p proposed in Appendix A. For purposes of general review a brief discussion of the applicable theory and the general Let, ^1 x„, denote the weighted average of x^^, . . ., equations is presented in the following. x,„„ where MULTIPLE LINEAR REGRESSION Let it be supposed that the following multiple linear (G-5) regression function is to be estimated: y = a + p^x, + p.,x, + . . . +p,„x,„ + V (G-1) in which Further, let the Oj^ element of the mth order determinant y= variable to be predicted (dependent); \A I be defined as V = random variable (error); (G-6) x-i jc,„ = measured variables (independent); and o, jS, /3„, = unknown (to be estimated). where j= 1, 2, ., m, The expected value (unbiased) is given by 1, 2, ., m, E(y) = a + p,x, + p,x,+ . . . + I3,„x,„ (G-2) and a*,t is defined as the minors of determinant \A\. If p Because the density of the random variable y is not is allowed to take values of 1, 2 m, we may express specified, the maximum-likelihood estimators of a and the the least-squares estimate H and of the constant term a, P's cannot be obtained. In these instances the least-squares and the regression coefficient fi^, as follows: method of estimation may be utilized. Since the application of these equations should yield the prediction of y at a future time from the current x values, one should collect a (G-7) set of observational vectors (,y^, x^, x^i, • • ., x,,,,), where y^ will be the past measured values of a quantity, which occurred at a later time than the x^^, x..i jc„„ mea• (G-8) surements, where the sub-i indicates the time at which the j)=i observations were made and the time to which the predic• Hence, based on the number (i.e., m) of predictors (ex• tion applies. It is upon this set of measurements that the planatory variables) required for an individual quantity, estimates of a and the regression coefficients, p, in Eq. G-2 y, one may use Eqs. G-7 and G-8 to estimate the un• are based. In particular, the solution to the following knowns of Eq. G-1. equations will yield the desired estimates of the coefficients: Minimum = 2,oV,= USE OF AVERAGES AS PREDICTIONS = -s,^iy,-a-p,x^,- . . . -p,„x,„i)- There are various types of averages which at first inspec• (G-3) tion appear to be good predictions in general. However, where the characteristics required are dictated by the unique ap• plication; namely, to predict certain traffic quantities at S«,{ } = the weighted (average) summation of { } various intersections within an urban area for use by a over past measurements (defined later). digital computer in making real-time control decisions. { } = an estimate of { }. With respect to this application, the properties of these 61 averages (and predictions in general) appear to be as pre• which may be simplified by rewriting the denominator sented in the following. The averaging (prediction) tech• (infinite series) to express its limiting value; namely, niques should: (l+P + p-^+p'+ . ..) = (!-p)-i (G-12) 1. Include as many of the past observations as practical; Substituting Eq. G-12 in Eq. G-ll gives 2. Weight the observations in order to give more im• portance to the most recent observations than to the "most past." y=(l-p)2p.y, (G-13) 3. Require simple calculations in order to minimize computer size and solution time (real-time applicability). It should be noted that y is employed as the prediction of y 4. Be able to include the most recent observations with• (namely, y) during a future time (i.e., J = y). Hence, the out complexity (i.e., easily updatable). following may be defined, to denote the time-series of pre• dictions: In view of the foregoing, an exponentially weighted moving average is proposed for use in predicting various y^ = y^ — Prediction of y, which includes the observations traffic quantities. These averages have been widely used y„ to y^, inclusive; and for the operation of inventory control systems. These ex• 5i = yi = Prediction of y, which includes the observations ponentially weighted moving averages are used to extrap• ^1 *o yjL> inclusive. olate a sales time-series (forecast sales), because they can be made quickly, easily, adaptable to electronic com• puters, with a minimum amount of information, and to Rewriting Eq. G-13, with the objective of developing a introduce current sales information (//). Further, Miller recursive equation to be implemented by a digital machine, (4) presents some empirical studies which to some degree gives validate the application of such averages to the predictions of certain traffic quantities needed for urban signal control. y„ = (i-p) (G-14) EXPONENTIALLY WEIGHTED MOVING AVERAGES or In general, the weighted average of y may be expressed as yo = (i-p)3'o+(i-p) Xp'y. (G-15) _ Woj;,, + H-iy, + . . . +w^y^ 1=1 (G-9) + w. Examining the second term on the right side of Eq. G-15, or (1 - p) J^p' y, = (1 - p) 2 P p"-" y. (G-16) 1=1 1=1 (G-IO) Upon further reflection, the term in brackets is merely the where previous prediction, y^, which does not include the current measurement >>„. Therefore, Eq. G-17 becomes w,„ w, w„ — arbitrary non-negative constants, called weights; yj = past observations of y; and (1-p) Jp'3'. = py, (G-18) 1=1 / = 0, 1, 2, . . . , ^, where y„ is the most current observation and y^. is Finally, Eqs. G-15 or G-13 may be expressed as the most outdated observation used (G-19) inEqs. G-9 and G-10. yo= ii -p) yo + pJi or, in another form, The exponentially weighted moving average is defined as follows: % = y.) + p (?! - yo) (G-20) Let w„, w,, . . . , w^=p'',p^, . . . , respectively, In words, Eq. G-20 states that in order to update the where 0 INCLUDING THE EXPONENTIALLY WEIGHTED Now, a partitioned-column matrix whose elements are MOVING TECHNIQUE IN THE MULTIPLE those contained in Eqs. G-24, G-25, G-27, G-28, and G-29 LINEAR REGRESSION MODEL (i.e., Cases 1 and 2, respectively), is denoted as follows: Recalling Eqs. G-5, the following define the weighted sums (G-30) ofx,„ , where and *2 necessarily all column matrices, or, more precisely, * = [y.^uyi^ii-ti,^ i y\-^u x.,ix,,x,, x.,y, x^^, ^li'-t.r]'^ * y 1'~ y ' (G-21) case 1 case 2 (G-31) P ^mi where T denotes the matrix transpose. Now, writing the recursive equation (i.e., updating the ex• where the weights are again exponential, and Eq. G-21 is ponentially weighted moving averages) for the general the exponentially weighted moving average of the predictor matrix where s denotes the case number (i.e., s=\,2, variables, Xj,,..., x^i. . . . ) the following is obtained: In general, the term ( ) included in Eqs. G-3 f 2„ *') = *'<=T:.im.:NT + P /f 2» through G-8 can now be defined as follows: \ t /ri'DATKI) 1_\ , /I'KKVIOUS -*'cri{iiEXTl (G-32) (G-22) In the cases previously discussed, j = 1 and 2. The Therefore, when one seeks to update the estimates of the number of individual (non-matrix) updating equations regression coefficients, ^j,, it becomes apparent, on expand• necessary would depend on the number of explanatory ing Eq. G-7, that the inclusion of the most recent data is variables. In the aforementioned cases (1 and 2) it would affected by updating various exponentially weighted moving require 4 and 8 (i.e., number of elements in *i and *-) averages. The number of terms required to be updated at equations, respectively. any one time for a particular prediction, y,, will depend on the number of predictors found necessary to be included PROPOSED PREDICTION MODELS in the particular regression model for y. Assuming the general subnetwork q, r, s, t, u (Fig. E-2) SOLUTIONS—s:, p. with the current state of signal q given as <^K1X,S. the following suggests particular prediction techniques for This section presents the expanded solutions for 5 and p^,. many of the quantities developed in the equations of Ap• Two cases—namely, simple linear regression where m — I pendices D and E. (Case 1) and multiple linear regression where m = 2 (Case 2)—are given. <^UlK,W For Case 1: The predicted duration of the next red phase (in sec• onds) may be obtained from y = a + |8i JCi (G-23) {y = S;-f|3,Jc,}*K:.=,w (G-33) (G-24) where y^w.n is the prediction of the duration of the next red phase (in seconds) as displayed to the east-west legs; )8t = -; (G-25) and, X'I'K\Y. W is the observed number of vehicles, queued on the opposite legs (combined, north and south) at the in• stant (|>,J:K,W„„„ has elapsed. For Case 2: AlE.W y = Z + p,x, + X, (G-26) The prediction of that part of the amber phase that may a=y-p,x,-^,x^ (G-27) be considered as an extension of the red phase (i.e., during which zero flow occurs) may be obtained from the follow• ing average: Pi (G-28) (5r = S}*'A,„,,v (G-34) where y'l>\]v..w is the prediction of C^'AIE.W. in seconds, ^21 2^10 •^11 •'^"^ 2/"" y^ and S^'AIE.W is the exponentially weighted moving average of the past measurements of (^'AIE,W However, one should note that <^'A|I,;,W is not directly observable with the pro- 63 posed instrumentation and therefore must be calculated. ture rates for consecutive cycles. It should be noted that Because the duration of the amber phase, 'AIIO,W. is the summation (for the foregoing average) as presented known (i.e., in general its length will not be varied from inEq. G-13 (namely, ^^'^^^has the interpretation that / cycle to cycle), the calculation of the past <^'AIK,W values assumes all the values of past cycles. should be performed as the difference between the total The aforementioned prediction of rf,,; has the advantage duration of the amber phase and that portion of <^vi en• of being simple and also yielding values which apply a full during which the stop-line detector measures a non-zero cycle in the future. However, it is believed that better pre• vehicular flow (i.e., departures). dictions of f/,.; may be necessary in certain applications to the equations (i.e., Eq. D-8). Hence, the following multi• h:,-w ple linear regression, which linearly relates both the number The lost time, as defined, is attributed to the starting of vehicles in queue and the measured departure rate (dur• transient and may be predicted as follows: ing the previous time interval) to the prediction of the departure rate (during the subsequent intervals), is pro• (y = a)'Ko. »» (G-35) posed: where yV. .,i » is the prediction of the lost time, in seconds, (G-38) which occurs during the first few At intervals of the phase •71 + li,x, + p,x^)",. GiK,w; and S'K ..r « is the exponentially weighted moving where ^''i. is the prediction of the departure rate for a par• average of the past /,,; or /^v values. ticular interval of the current phase; JT/'H is the observation Again, /,,. ,„. is not directly observable with the proposed of the number of vehicles in queue at the time the predic• instrumentation and therefore must be calculated. These tion is made; and x,'h. is the observed departure rate (cur• calculations will be performed on the past departure flow rent). It is believed that the general form of this prediction rates for the starting-transient period and the measured model would be necessary at intersections where there are saturation flow rates from the same intersection. left turns with the associated conflicts. Let d'f, be the measured saturation flow rate from the east leg; rf^j,. the calculated average value of departure rates from the east leg during starting transient; and TM the Inasmuch as arrivals at an urban intersection are usually observed duration of transient. Then the direct result of some control decisions (i.e., traffic sig• nal displays), it may be possible to relate the arrivals at /,.: = ^rAr-^^|' TAf^ (G-36) one intersection to the control decisions and departures of another (4). It should be generally noted that the a,,.; Note: If the vehicles accelerated instantaneously (i.e.. terms considered in Appendix D and Appendix E are those arrivals to the end of the existing queue or, in the case of zero queue, the stop line. Therefore, because the predictions obtained in the following by the proposed technique are made at the approach detector, they must be extrapolated Two methods for predicting flow rates are proposed. to the end of the "observed" queue in order to be applicable The first simply uses the exponentially weighted moving to the minimum-delay equations. The arrivals at point 1 average of departure rates over corresponding intervals (e.g., to the east leg of intersection q) of Figure G-1 are (referenced from the start of the green phase) of consecu• seen to be the result of straight-through movements from tive signal cycles, as follows: the east leg of intersection s during ^ © Figure G-1. Arrivals to q from s. 64 (G-39) or Nis + *s(«s - ds)£it ^ 0 (G-48) where y«B= prediction of the arrivals at point 1, for a subse• Nis + {*'s«s - (*'s - n)^8}A/ ^ 0 (G-49) quent cycle, during a particular number of intervals Setting Eqs. G-48 and G-49 equal to zero, and solving for after the start of phase 8<^GIE,W (or BG|N,S)'> and and ^'g, respectively, gives XI'K = total number of vehicles which desired service at q during the most current phase .(^GIE.W (or BGIN,8)- ksAt = (G-50) (."a — ds) It should be noted that X^'E may be calculated by summing the counts as obtained by the detector at point 1 for con• and secutive periods. Alternately they would apply to the re• {Nia + nAtds) sults of g<;.GiE.w and B<^G|N,S- k'sAt = (G-51) («s-^8) SOME SIMPLIFICATIONS OF THE DERIVED EQUATIONS As a result, Eq. D-12 becomes Before proceeding to discuss certain predictions within the — nAt ds (G-52) context of the individual equations, it is in order to further At{k'a-ks)=At,s = ^_ reduce the form of the equations, through both algebraic manipulations and reasonable simplifying assumptions. Similar equations may be obtained for the north leg (i.e., Also, a few equations as presented in Appendix D are and AfgN)- generalized to consider an extension of n\t. Rewriting Eqs. D-14 and D-15, using the foregoing, gives Odec s = K,{k's - ks)asAt (G-53) Isolated Intersection {Appendix D) Substitution of Eq. G-52 in Eq. G-53 gives Generalizing Eq. D-2 for an extension nAt gives _ (- nAt rfg) (G-54) Diec s - ^1 =— Os ASD = A^^i^tE A'i + dijff Ar<)| (^RlE.W + S^ AlE.W + ^S.w) {as — «s) (G-40) Similarly, (- nAt ds) _ which, through the use of average values of dt (denoted (G-55) by 3) over the period nAt, simplifies to {as-da) AISD {nAt (^B + dyf)} (?niB,w + ?'AIE,W + 'E,W) Analogous equations may be written for the north leg (G-41) (i.e., Z)de<; N and D„ecN)- Generalizing Eqs. D-4 and D-5 gives Subnetwork of Signalized Intersections {Appendix E) Rewriting Eq. E-1 la gives AV. = |(^X«'«^''J+^-Ef-^'^-J^ (G-42) nAf -2{a,-d,)'~J^N,aAh + A5,w={(2«iwA^)+yV..|^^i^ (G-43) in" / / -v m« ., 2 (G-56) Reducing the form of Eqs. G-42 and G-43 by employing the average values of a, over the period LAt and df over the By using the relationships that Nigy is invariant over values period nAt {a and d, respectively) gives of / = 1, 2, 3 . . . K", Ati = At, for any values of / = 1, 2 (nAtdu') . . . and 7=1, 2 . . ., and the simplifying assumption that AV. = A{La^At + A^rE) J (G-44) the arrivals occurring over the interval AfAf (at intersec• tion r) may be included as their average over the interval K'>At, the following expanded form of Eq. G-56 is ob• A5,W = {£.«wA< + (G-45) tained: -\,rD\, = N,sK<'at+{l+2 + + K'>) Rewriting Eqs. D-10 and D-11 and simplifying yields Af= X (as - da)At^ - K«(Sg-rfg) — Ni8 + 2 «isA^. - X '^.sA'i ^ 0 (G-46) 1=1 1=1 -wW.gAf-Kl 4-2-F + m<>) -r A«= A^78 + 2 - ^ d,sAt, ^ 0 (G-47) X dsAf= - m«da (G-57) 65 ® © Figure G-2. Intersection pair g,J. But q arrives at the tail end of the queue on the west leg of intersection s may be obtained from .+^ = ^<^ (0.58, vnAt = - L[sNovf + (flw - dy,)nAt} (G-60) which rearranges to so Eq. G-57 may now be rewritten (rearranging and com• bining terms) as 6,-2 — Lf^N ow n\t — - (G-61) D\^ = N,^(K<>-m'>)^t V -1- iLs(aw — ''w) For the last vehicle from q, + as + ds 2 / ^' (G-59) vn'M - - L{sA^ow + s(«w - ^w) (« + «')Af} which is dependent on the average values of and being (G-62) unchanged over various time intervals (e.g., K'>At, m^AO- which simplifies to Although Eq. G-59 is a simplified form of Eq. G-56, the general form is applicable to the D'l'it, D*A, and D"^* delay — L{sA^oy -I- (uyi — dy.)nAt} n'At- (G-63) terms. V 4- L(a^v - dy,r) One may now write CRITERIA FOR EVALUATION OF M MAt= {n + (n' — n)}At (G-64) The equations developed in Appendix E allowed for the Hence, if departures released during «Af from an intersection to arrive during some different time interval MAt at the down• n'>n, M>n (G-65) stream intersection. The M" term is first introduced in or, if Eq. E-12 to allow for the fluctuating queue length at the (G-66) downstream intersection. n' APPLICATION OF PROPOSED PREDICTION NOMENCLATURE AND DEFINITIONS Figure G-3 represents a time series of signal-cycle lengths y = variable to be predicted; of two faces (out of four) of a signal at intersection q, V = random variable; where ^y/K, ,y,<*G, ^y^A represent measured phase lengths JCi jr„j = predictor variables; of <^R. G. and 2 H 1 U 0 H Figure G-3. Time series of signal cycles at intersection q. 67 5'^ or j-i = a prediction of y which includes the a*'AiK,w — an average of past measurements of observations y„ to y^^; <^'AIE,W; y, or Jo = the last prediction of y, which where a'B = an average of the past measurements referenced from the current instant in• of/E, cludes the observations y^ to y^; d's = measured saturation flow rate from *s = a matrix whose elements are required east leg; to be updated in order to update the d^B = calculated average departure rate dur• estimates of a, ;8,„; ing starting transient (east leg); {A + BY = A'" + Bt TAt — observed duration of transient; y'^HiE.vr = equivalent to ^KIE.W'. 6,_2 = distance between detectors 1 and 2; .Vj'^HiE.vr = observed number of vehicles queued L = average length of vehicle plus average on the opposite legs (combined north headway; and south) at the instant APPENDIX H APPLICATIONS OF THE HIGH-SPEED DIGITAL COMPUTER IN CONTROL OF TRAFFIC Because the tasks that may be performed by a digital com• different control systems, networks, and constraints. These puter are in general limited only by the ingenuity of the degrees of realism will depend on the available knowledge individual developing the program logic, it is not surprising pertaining to the real situation, the approximations and/or to find that the general purpose high-speed digital computer assumptions permitted, and the philosophy used in the de• may be employed in the control of traffic at various levels. velopment of the model (e.g., macroscopic vs microscopic For example, the computer may be used to find solutions representation of traffic). to particular network configurations as a function of various The computer also presents itself as an excellent tool to traffic parameters by modeling the traffic and control strate• be used in directly controlling actual traffic signals in real gies for laboratory experimentation. This technique is com• time. In this function the computer would generally per• monly described as a simulation of the traffic network and form calculations to determine the value of the control its related control logic. parameters, decode information as presented to it by the Although most of the work in this field has been con• vehicle detectors, and transmit the coded solution through cerned with the "degenerate network" or the isolated inter• the communications network to actuate the local signal section, there have been some simulation studies for a num• controllers. In the hypothetical direct application of simu• ber of signalized intersections. With the currently available lation results of an intersection controlled by a fixed signal computer hardware and software, it is evident that the cycle, the control computer may, instead of its calculation computational complexity of the problem is formidable for role, serve as an accounting device. This device has the a large network. Nevertheless, it is conceivable that, given capacity to memorize large quantities of previously obtained any physical realizable objective function (i.e., minimizing solutions and change the cycle length and split according delay, minimizing queue lengths, etc.), an optimum solu• to the current traffic information presented to it. tion may be found through computer simulation. In its function as a control unit, the computer may be Because these solutions yielding cycle length, splits, off• programmed to emulate the operation of any number of sets, etc., vary as a function of the values of the traffic special purpose traffic controllers (full traffic-actuated, pro• parameters, the control of the real network of signals must gressive, etc.) Without extending the emulation concept depend on a knowledge of these parameter values or some further, advantages may be gained merely through the other related function. Further, it should be noted that limi• flexibility of being able to apply various controls to sub• tations which are inherent within the modeling of the vehic• networks that may be redefined in terms of configuration ular dynamics, human reaction, control logic, etc. (when and intersection content as the traffic flow warrants. In compared to the real situation) will, in part, determine the addition, the input constants (minimum green, maximum validity of these solutions when applied to the given net• red, offsets, splits) that are normally entered mechanically work. It is apparent that various degrees of realism in the at the local controller may now be varied from the con• building of a model are required for obtaining solutions to trol site throughout the day as conditions necessitate. Ob- 68 solescence, as experienced with the purchase of special pur• control (which is now in existence or yet to be developed), pose equipment through incapabilities of the selected con• and (d) process large amounts of traffic data in order to trol system to meet changes in ordinances, new signal reveal a posteriori an existing system's performance. How• phases, road construction, or simply the changing vehicular ever, it must be reemphasized that the validity of the results flow* patterns, is virtually eliminated. obtained from any simulation, control, or data analysis It is apparent that this technique of emulating existing operation obviously will not be proportional to the capa• traffic control equipment is not using the computer opti• bilities of the machine. Rather, it will depend on the validity mally, because the very nature of the control philosophies of the concepts and theories put forth by the individuals employed is limited by the mechanical-electrical equipment using the tool. selected. To utilize the computer's capabilities to efficiently This appendix defines a number of conventional control control the traffic signals within a network, it is suggested strategies {18, 19, 20, 21, 22), then presents the control that once a criterion, or set of criteria, has been found it logic in the form of a flow chart which may be programmed should be implemented as a general set of equations that for the digital machine. Also included is a discussion of account for information obtained on the dynamic traffic more academic interest concerning computer simulation characteristics. Hence, by optimizing the objective func• (7, 17) and its direct application to control. tion within the constraint equations, one may develop an adaptive control system. It should be noted that simulation SIMUUTION techniques can prove to be a powerful tool in both the "emulation control" and the more general adaptive system. Simulation techniques are capable of providing the traffic By building a model to simulate the particular control logic, analyst with the necessary number of traffic hours at pre• detector locations, boundary values, etc., may be investi• determined conditions in order to obtain good estimates of gated. the mean values of the variables of interest. Also, they are In further applications, as in using the computer as a able to provide for rapid and easy changes in the control data processing tool for post-analysis studies, large quan• logic and traffic conditions within the program. tities of real traffic data obtained by automatic data gather• For purposes of illustration, the simulation of an orthog• ing equipment or human observers may be analyzed quickly onal intersection of two, two-lane, two-way streets (Fig. and efficiently. The results of such analyses are particularly H-l) is examined to determine how the results may be important if the "figure-of-merit" of the particular control applied to the control of real traffic signals. In the simplest system (e.g., fixed-time or adaptive control) is not calcu• case the signal is assumed to be of the fixed-time type (pre• lated as part of the controlling process. determined cycle length, split, and amber). The simulation As a result, computers may (a) be employed in obtaining runs would be made in order to find the optimum solution a solution a priori for a specific network for a set of traffic for a given set of traffic parameters. As the traffic condi• parameters, (b) aid in the implementation of previously tions vary the values of these traffic parameters will, in determined solutions, or (c) implement any other form of general, yield different solutions. Figure H-2 shows typical traffic parameters that may be considered in determining * Caution should be observed in the interpretation of this sentence Obviously, when appreciable increases in the efficiency of the flow of traffic the most effective signal setting. Each of the four approach through control have brought that flow to saturation, only construction of legs has associated with it four levels of approach volumes new highways and/or restriction of vehicular use will solve the traffic problem. and two levels of turning percentages per movement. The possible permutations of the parameters of the four legs taken at one time involve 65,536 distinct cases requiring solutions. The number of traffic hours required to obtain a solution will depend on the number of hours required per control setting (to obtain the mean value of the objective function) and the number of individual control combina• n tions considered to be feasible solutions. By multiplying the number of traffic hours required by the simulation computer time per traffic hour one may obtain the total amount of computer time necessary to obtain the solutions. The simulation time (computer time per traffic hour) will be a function of the complexity of the model, the program• ming techniques employed, and the characteristics of the computer used. As an example, one "fairly complex model" (7, 17) run on an IBM 7090 computer to simulate conditions at a pretimed isolated intersection is examined. Only 0.5 sec of computer time was required to simulate 1 hr of traffic time, which gives a simulation time (computer time/traffic time) of approximately 1:7,200. Hence, if 144,000 traffic- Figure H-l. Orthogonal .signalized intersection of two 2-lane, hours were required for the set of solutions, approximately two-way streets. 20 hr of computer time would suffice. By taking actual 69 VOLUME LEVELS TURNING MOVEMENTS VOLUME LEVELS TURNING MOVEMENTS LEFT RIGHT LEFT RIGHT n(l) x,(') Y(') • • • Y(*) a APPROACH LANE #1 APPROACH LANE m Qa APPLIES IF O^Q 6 VWERE, Q' = VOLUME (VEHICLES PER HOUR) Qj, APPLI ES IF Oa^ Q volume counts and turning movements at the intersection, may be introduced as a function of current speed, road• the optimal signal setting choice may be selected from the way conditions, weather conditions, etc. This concept of simulation results. However, the solution would be applica• applying current traffic control techniques by programming ble only under those same traffic conditions. Another way a digital computer to vary the mode of operation of any to apply the solutions would be to have the control com• intersection and its interrelation with the surrounding sig• puter store them on magnetic tape or disk and select the nalized intersections presently is being applied in cities like one which corresponds to the traffic conditions, as currently Toronto, Canada, and San Jose, Calif. sensed (Fig. H-3). Although this method is only of aca• demic interest (since better results Would be obtained from Glossary a traffic-actuated controller), it is practical in the sense that it would take only a small fraction of a second to obtain The following definitions are used in this section as applying the stored solutions and implement them through com• particularly to conditions of semi-traffic-actuated control: mands sent over a communications network. Major-street minimum green interval—the minimum amount of time during which the green signal indication is SEMI-TRAFFIC-ACTUATED CONTROL displayed to the major street before the right-of-way can be transferred to the minor street. If actuation occurs after The semi-traffic-actuated form of control is usually applied this interval has expired, the right-of-way will be transferred to an intersection of a heavy-volume (major) street with a immediately. relatively low-volume (minor) street. The signal is nor• Major-street amber interval—the time allowed for the mally green on the major street and will respond to actua• major-street traffic to clear the intersection before the move• tions on the minor street after a predetermined minimum ment of minor-street traffic. green interval has elapsed. Hence, detectors placed only Minor-street initial portion of green interval—the time on the minor street may serve not only to change the signal allowed for queued vehicles to get into motion. from its normal state, but also to determine the length of Minor-street extendible portion of the green interval— the minor street's green phase within the limits of the pre• the amount of extension following each detector actuation determined minimum and maximum. Because there is no after the initial portion. information concerning major-street traffic, the effective Minor-street extension maximum—the limit set on the use of semi-traffic-actuated control is limited. The limita• extendible portion of the green interval. tions for the case in which this special purpose hardware Minor-street amber interval—the time allowed for the is installed would be determined at the time when the minor-street traffic to clear the intersection before move• volume was heaviest on the major street. In the case of ment of the major-street traffic. applying a computer program to implement the logic of the aforementioned hardware, the major-minor street volume Operation conditions, obtained historically, would determine those portions of the day during which the control would be With no minor-street actuations the signal will remain effective. In the control of traffic by the computer, many green on the major street. When an actuation is detected forms of control may be assigned to various combinations the major-street amber interval will be displayed before the of signals (subnetworks) as a function of changes in the right-of-way is transferred to the minor street (after the dynamic traffic pattern. Furthermore changes in the pre• expiration of the major-street minimum green interval). determined minimum, maximum, and extension intervals Minimum minor-street green will be assumed to consist 70 PROBLEM DEFIN ITION OPTIMAUITY CRITERIA TYPE OF CONTROL RESTRICTIONS t CONSTRAINTS TRAFFIC-DATA SOURCE PHYSICAL RELATIONSHIPS SUB-NETWRK CONFIGURATIONS "MODEL BUILDING" COMPUTER ilMUJLATI^N_ GENERATE N TRAFFIC-HOURS PER FEASIBLE SOLUTION (CONTROL PARAMETERS) VARY VALUE OF TRAFFIC AND CONTROL PARAMETERS SELECT (STATISTICAL) OPTIMA STORAGE OF SOLUTIONS* COMPUTER DECODE INCOMING TRAFFIC DATA SOLVE PROGRAMMED CONTROL EQUATIONS USING PREDETERMINED SOLUTIONS DETERMINE THE CURRENT PHASE LENGHTS ETC. TRANSMIT INFORMATION TO COMMAND LOCAL SIGNALS TRAFFIC DATA COMMUNICATIONS LINK URBAN STREET NETWORK VOLUME IIGNALI PRESENCE GAP LENGTH ISOLATED SIGNALIZED INTERSECTION ETC. INTERRELATED SIGNALIZED INTERSECTIONS (SUB-NETWORKS) •"SOLUTIONS" MAY BE DETECTOR LOCATIONS, MAXIMUM OR MINIMUM CYCLE LENGTHS IN THE ADAPTIVE CONTROL CASE OR PHASE LENGTH, SPLIT AND OFFSET IN THE "FIXED" TIME APPLICATION Figure H-3. Role of simulation in real-time control of traffic signals. of an initial and an extendible portion of the green inter• interval for minor-street clearance is extended in some val. Only actuations occurring during the extendible por• available systems. The semi-vehicle-actuated intersection tion will affect the timing. Each succeeding actuation can• may be interconnected into a progressive system such that cels the unexpired time of the previous extendible portion the minor-street green is only permitted in the system cycle and adds another full extendible portion. This sequence of when it will not disturb the predetermined artery progres• events (Fig. H-4) will continue until either an extendible sion. period has elapsed without further actuation (decrease in the demand) or the minor-street maximum extension is Nomenclature exceeded. In either case the minor-street amber interval will be initiated before the right-of-way is transferred to the The following symbols are used in this section as applying major street. In the latter case, the right-of-way will be particularly to the logic and programming for the conditions returned to the minor street following the expiration of of semi-traffic-actuated control: major-street minimum green interval. Also, the amber A = the major street; NPUT/INTERSECTION HO / ACTUATIOB ON B LEGS? TERMINATE CURRENT (>s g ACTUATION ON PHASE ' 9 LEGS? ACTUATION OF ft/.*"'* B LEGS' TERMINATE CURRENT INITIATE 0m PHASE NO / fW"* TERMINATE CURRENT PHASE IN TIATt TERMINATE CURRENT PHASE INITIATE PHASE Figure H-4. Two-phase semi-vehicle-actuated controller. 72 B: the minor street; Extendible portion of the green interval—the time ex• tension which follows each detector actuation after the Q<^*G1A = elapsed green time on major street, A, for intersection q at any instant; initial portion has elapsed. elapsed green time on minor street, B, for Extension maximum—^limits the amount of time for the intersection q; extendible portions of the green interval, after an actuation is detected on the opposite phase. q<^GIA mln ' major-street minimum green interval (in• tersection q); Amber interval—the time allowed to clear the intersec• tion before the right-of-way is transferred to the other q<#>AlA = major-street clearance intreval (intersec• tion q); street. q<#>'*GIB = minor-street initial portion of green; minor-street extendible portion of the Operation green interval; When the right-of-way is first transferred, the minimum minor-street extension maximum or MaXq(A<^G!B) = green time which must be displayed consists of an initial interval and one extendible interval. Detector actuations minor-street clearance (elapsed time); QG]B'> be transferred at one of the following times: and 1. Immediately if the extendible interval has expired. time, referenced from the initiation of the V*G1B = 2. At the expiration of the current extendible interval phase, of the most recent actuation on B. if no other actuations are detected before it expires. 3. At the expiration of the maximum green interval if FULL-TRAFFIC-ACTUATED CONTROL successive actuations are received on the street which now The full-traffic-actuated control is selected for intersections has the right-of-way and they are separated by less than where traffic demands on all intersecting legs are considered the extendible interval. necessary information in order to provide for the efficient It should be noted that the maximum green interval is operation of the signal. Detectors located on all the ap• referenced (zeroed) from the time of the first actuation on proaches to the intersection serve not only to assign the the cross street. If the current phase is terminated due to right-of-way but also to determine what the phase length the expiration of the maximum green time, the subsequent should be. This phase length will fluctuate between the amber interval will be extended and will be returned to the predetermined minimum and maximum values, depending initial state after timing maximum green (as if the last actu• on the length of time between actuations on the street hav• ation had occurred during the initial period). ing the right-of-way and the demand on the cross streets. Hence, the right-of-way is switched from street to street, Nomenclature depending on the frequency of gaps which exceed the predetermined time lengths for each street. As volumes in• The following symbols are used in this section as applying crease gaps occur less frequently and the traffic-actuated particularly to the logic and programming for the condi• signal operation approaches that of pretimed signals with tions of full-traffic-actuated control: the phase lengths equal to the predetermined maximums. initial portion of the green interval for The added flexibility of allowing for the variability of the ''GIB- legs A and B, respectively; predetermined gap interval during a particular phase makes extendible portion of the green interval this form of control—namely, the traffic-density full-traffic- A(^GlA' A(/)GlB = for legs A and B, respectively; actuated control—much more sensitive to fluctuating traffic demands. For example, the decrease of the gap interval Max (A<;>GU)> extension maximum for the extendible may be made proportional to the size of the queues waiting Max (A''AIA. '^<#>AIB- and B, respectively; trol: an extension of the minimum clearance Initial portion of green interval—the time allowed for A<^>A1A. A(^A1B • interval (extended only if maximum the queued vehicles to get into motion. timer has operated or if detector actu- INPUT/IKTEIISECTION (J) HAS THERE BEEN THERE BEEN YES /ACTUATION>«v^ ON B LEGS? •N tCTUATION ON AN ACTUATION ON A LEGS? B LEGS? LEGS? ACTUATION ON ACTUATION ON B LEGS? A LEGS? UPDATE UPDATE X X ACTUATION 0N> ACTUAT A LEGS? LEGS? INITIATE INITIATE INITIATE \ RETURNING TO \ INITIATE INITIATE .*»/» INITIATE *.„ WITHIN / RETURNING TO "ITHIN < ^Vi'-^Y'**" Figure H-5. Two-phase full-vehicle-actuated controller. 74 ation is received during clearance in• tive indicator of the predominant flow, or more precisely terval); and the congestion, may be obtained by taking the ratio of the ''A<^*G> "H'^'G = "'"s of actuation (into green phase) inbound or outbound lane occupancy to their sum. on legs A and B, respectively. Hence, the indicator may be expressed as 1/(1+ 0), where / and O represent the inbound and outbound lane COORDINATED CONTROL SYSTEMS occupancies, respectively. For example, if / > O then the The object of coordination is to establish a relationship comparative term becomes greater than 0.5; similarly, if between the start of the green phase at two or more inter• 1 = 0 then the term is precisely equal to 0.5. From pre• sections along a major street or in a network of streets. determined classifications the system will operate on either There are several forms currently available for linking an average or a preferential offset mode. That is, for some the intersections on a main traffic route. The simultaneous, value of //(/ -I- O) >0.5 the system will select an inbound or synchronized, system and the alternate, or limited pro• offset, for some value of //(/ + O) < 0.5 the system will gressive, system are two of the most elementary forms of select an outbound offset, and for the values between an coordination. In the former case all signals along the average offset will be implemented. The only exception is controlled street display the same phase to the same traffic when the values of lane occupancy for both inbound and stream at the same time. In the latter case adjacent signals outbound traffic fall below a predetermined minimum. This present opposite phases alternately along a particular street. restriction does not permit the system to fluctuate between Variations on the systems may be made by applying the inbound and outbound offsets for small traffic variations, aforementioned progressive systems to adjacent groups of and therefore adds to performance stability. signals. Having selected one of three offsets (inbound, outbound, However, the progressive system, as it is commonly or average), the computer is prepared to select the common called, provides for the cycle time for each intersection in cycle length (Fig. H-6). For the case of preferential offset the system to be fixed, although the green phases are dis• modes the computer calculates the total duration of the placed with respect to each other according to the desired cycle to be implemented by computing the level of lane progression speed. This system may be used to give prefer• occupancy determined by averaging the two sampling de• ential movement in favor of inbound flow at the expense of tector outputs from either the inbound or outbound lanes. the minor flow traveling in the outbound stream, or vice In the case of average (nonpreferential) offset the com• versa, as conditions warrant. In general, the series of sig• puter accepts information from each of the four detectors nals to be coordinated may be of the semi-trafflc-actuated and calculates an average value using the inbound and out• type, in which case a supervisory background cycle is im• bound occupancy measurements. Based on the value ob• posed on the signals. This serves to assure that each of the tained as a result of the aforementioned lane occupancy semi-actuated controlled intersections provides a minimum averages, the computer will decide to which of six prede• green phase in a time relation (offset) best suited for the termined levels of lane occupancy the calculated average progression speed in a particular direction. In the case where there is no demand detected on the minor street, belongs. This then determines the cycle length, as previ• those intersections are permitted to operate as isolated ously assigned to each level. vehicle-actuated signals contingent upon the condition that Lane occupancy as previously defined is equivalent to there is no interference with the prescribed plan of pro• the measurement of the percentage of time during which gression. The following is a description of a special pur• a vehicle is sensed by the detector. Because these measure• pose system similar to the one now in operation in Buffalo, ments must themselves be averaged over a particular inter• N. Y. val of time, say x minutes, this average may be denoted as a moving average which will determine the percentage of Operation the last X minutes during which the associated detectors were occupied. The resultant values of lane occupancy may Control decisions are based on lane occupancy {18, 22), be made more sensitive (quicker response) to the state of a factor obtained from the common presence detector by increasing congestion than to that of decreasing congestion calculating the ratio of the total accumulated vehicular by permitting different adjustments for the sampling interval. passage time measured during a predetermined time interval to the total elapsed time of the interval. It is believed (22) Further constraints that provide for over-all insensitivity that such a quantity results in a more significant measure of to instantaneous fluctuations in traffic (greater operational congestion than does density. The system is designed to stability) are to set values for the maximum frequency of control the cycle length, offset, and split for a number of changes in offset and require the system to pass through signals along a major arterial. Four detectors are proposed the average mode when transferring between the inbound to obtain the necessary control measurements, including and outbound modes. two detectors sampling inbound traffic and two detectors sampling outbound traffic. Nomenclature In general, the common cycle length will be selected by considering the level of the calculated lane occupancy, and The following symbols are used in this section as applying the offset will be chosen as a function of the relative values particularly to the logic and programming for the conditions of inbound and outbound lane occupancies. Such a rela• of coordinated (progressive flow) systems: 7 / .n / N. I CALCULATE. INPUT L »/i'«j„,VL^^D'^o„,VJ!^ ,'--iL ^\ / / I V*0' SET J = J » I SET J = J * FOR J = 1,2,3,*,5,6,7 FOR , = 1.2.3,11,6.6.7 / SET THIS VALUE \ /SET THIS VALUE \ SET J = J • 1 NO Of J TO j*SELECT OF J TO J* SELECT^ FOR J = 1,2,3,H,6,6,7 > Cj'FOR "INBOUND Cj» FOR OUTBOUND , \ OFFSET" / \ OFFSET / /SET THIS VALUE \ OF J TO J*, SELECTN Cj» FOR "AVERAGE / V OFFSET- / Figure H-6. Progressive mode; selection of offset and cycle length. 76 /* — average inbound lane occupancy; to outbound, average to inbound, in• O^— average outbound lane occupancy; bound to average, and outbound to average, respectively. i or -J. Ij or -j, O, „r -j = predetermined ranges from which to CONCLUDING REMARKS select cycle lengths, where / is one of 7 The main purpose of the preceding discussion has been to levels of occupancy, yielding 6 cycle comment academically on the application of traffic simula• lenths; tion to control, and to present a few of the most commonly Cfc — cycle length, ^ = 1 6; implemented traffic control strategies. Although these con• Cj;* = chosen cycle length for a particular trol doctrines are universally* employed through the use progressive mode; of special purpose analog hardware (22, 23, 24), their fi^, tj, t° = elapsed time of the current average, adaptation to the general purpose digital computer begins inbound, or outbound progressive with the flow-charting of the control logic. These charts modes, respectively; have been presented in Figures H-4, H-5, and H-6 for the ' mill » ' Iinii/ > particular modes described. minimum time for the average, in• bound, and outbound progressive The same control modes could be programmed for the modes; computer and, through an analysis of the street and traffic patterns, assigned to various subnetwork configurations for values of the inbound and outbound the city being considered. This would serve as a model for lane occupancies, respectively, such costing the control system designed to emulate conventional that the average offset mode is auto• control strategies. matically selected if /* and O* fall below; To have been consistent with the study performed for a digital-computer-controlled system using an advanced adap• pi: /*/(/' + o«); tive control logic as given elsewhere in this report, these threshold values that initially deter• costs should have been obtained. This course has not been mine the offset mode based on the cal• pursued, the principal reason being that the capabilities of culated P*; and the digital computer are not deemed as being adequately A-0> t^A-U threshold values which determine exploited, if it is used only to implement the more con• (after the minimum elapsed time) ventional control modes. the value of necessary before the * Exceptions may be found in the cities of Toronto, Canada, and San offset mode is changed from average Jose, Calif. APPENDIX I ANNOTATED BIBLIOGRAPHY As part of the synthesis of a digital-computer-controlled ACTON, F. S., Analysis of Straight-Line Data. Wiley (1959). signal network a number of documents dealing directly This book was written for the "statistically self-edu• with the subject of traffic control and also with other sup• cating physical scientist and engineer" who deals with porting subjects (statistics, computers, electronics, vehicular data containing one or more lines entrapped within dynamics, etc.) have been read with varying interest and his experimental variability. Emphasis is placed on completeness. It is the purpose of this bibliography to the analysis of variance as a mathematical tool. present a large portion of these documents and comment Deliberately omitted are some of the classical ap• briefly on their contents. A word of caution is in order, proaches that encourage an unthinking mechanical inasmuch as these comments are not intended to be either solution to the problem of straight-line fitting. academically objective, in the form of a book review, or academically subjective, in the form of a critique, but rather BECKMANN, H., MCGUIRE, C. B., and WINSTEN, C. B., Studies were written with a bias (i.e., a particular goal) as the in the Economics of Transportation. Yale Univ. Press documents were read. This goal represents the objective (1955). of the project (i.e., to synthesize a real-time digital-com• This book is addressed to analysts in various pro• puter-controlled signal system for a city such as White fessions, including economists, traffic and railroad Plains, N.Y.) If, indeed, the bibliography and comments engineers, management scientists, operations re• are of interest to others, this is a by-product and not the searchers, and mathematicians. Studies relating to intention of the author. highway traffic and railroad transportation are offered. 77 Of particular interest to the project is Chapter 1, within the limitations of this particular system's entitled "Road and Intersection Capacity," which ap• instrumentation. Results are given in terms of the plies queuing theory to such traffic situations as the average delay per vehicle and the defined "congestion." flow of cars through an intersection and the passing It should be noted that this performance was compared of slower cars by faster ones using gaps which occur with an existing fixed-time system with no indication in the opposing traffic stream. as to the nature of the particular signal settings or network considerations. BERKEI EY, E. C, and WAINWRIGHT, L., Computers, Their Operation and Applications. Reinhold (1956). Cox, D. R, "Prediction by Exponentially Weighted Moving Averages and Related Methods." Jour. Royal Stat. Soc, The purpose of this book is to present basic infor• Series B, Vol. 23, No. 2, pp. 414-22 (1961). mation about computers, particularly automatic com• puters. The authors realize that the development in This paper is a highly technical (mathematical) de• the field is so rapid that some of the information in velopment which assumes previous background in this book will shortly become out of date, but many statistics. The paper calculates the mean square error of the concepts and discussion of applications are still of prediction for an e.w.m.a. when the series is a current. Of particular interest was Section II, entitled Markov series. The optimum choice of the damping "Automatic Digital Computing Machines." constant is given, although not critical. There is a value of the Markov correlation below which it is BONE, A. J., MARTIN, B. V, and HARVEY, T. N., "The Selec• impossible to predict the local variations of the series tion of a Cycle Length for Fixed-Time Traffic Signals." with an e.w.m.a. A modified e.w m.a. having a mean Joint Highway Research Project, MIT Dept. of Civil Engi• square error approaching that for the best linear neering and Mass. Dept. of Pub. Works (Apr. 1964). predictor (Wiener) is formulated. This is of value if the Markov correlation parameter is negative and pos• This paper describes a general method for deter• sibly when the correlation parameter is near the mining the optimum cycle length for fixed-time signal• limit p„. ized intersections, using a combination of three criteria to evaluate various cycle lengths. The criteria are the delay per vehicle, the expected queue length, and FRENCH, R. A., "Coordinated Traffic Signalling System—Syd• the probability of entering the intersection during the ney, Australia." Traffic Quarterly, pp. 76-88, The Eno first green phase. Two examples are used to illustrate Foundation for Highway Traffic Control. (Jan. 1965). the application of the method and the use of the formulas. A computer program for calculating the This paper states that a control system responding aforementioned criteria is described. The techniques to vehicle detectors (as presently available) is not utilized were primarily due to Webster's work on adequate for the central business district. Particularly, signal timing, including the formula for the delay per it is argued that closed-circuit television, coupled with vehicle. It is noted by the authors that the engineer trained observers, is the most convenient and economi• must make the final decision as to the relative import• cal method for systems having about 100 control ance attached to each criterion at a particular location. points or local intersections. A system is described in detail, consisting of twelve cameras strategically mounted on high buildings in the central business CASCIAIO, L., and CASS, S., "Pilot Study of the Automatic district of Sydney, Australia. The basis of the traffic Control of Traffic Signals by a General Purpose Electronic control system is the coordinated operation of traffic Computer." HRB Bull. 338, pp. 28-39 (1962). signals at local intersections to minimize delay, con• sistent with safety requirements. The conclusions This paper describes the system concepts employed indicate that the installed system is operational and in a pilot study designed to control a network of traffic gives the results of the (desired) reduced travel signals (9 to 16 signalized intersections) by a general times. However, it is recognized that control depends purpose digital computer in Metropolitan Toronto. on the quality of traffic condition assessments made The purpose of the study was to demonstrate that the by the operator, and his choice of control programs. computer could be connected to an existing traffic There is a limit to the amount of information that the signal network to provide a greater degree of service operator can absorb and process at any one time, and and flexibility than was heretofore attainable with this could limit the efficiency of control achieved. the conventional (special purpose) control methods. The paper further states that vehicle detectors have Also, it was desired to learn from the study how the been placed experimentally in two sections of a two- system could be used to improve traffic flow, measure way street. such improvement, and provide data for post-analysis requirements. Vehicle detectors which were installed on most approaches and existing traffic signals were GARWOOD, F., 'The Sampling and Use of Traffic Flow Statis• connected to the central computer by telephone cables. tics." Applied Statistics, Vol. 11, No. 1 (1962). The paper briefly discusses the master control program stored in the computer which may assign various plans This article discusses two main sampling problems which in turn define a mode of operation for the which arise in traffic flow statistics. The first is that particular signals. However, no details are given as of the accuracy with which trends from year to year to the programs used, or the relative success of in• in the total amount of travel on the road can be esti• dividual control philosophies that were simulated or mated from continuous counts at a sample of points newly developed for the system. Also included is a on the road system. The second is concerned with discussion of platoon structure, delays and congestion sampling in time at particular points and the effect of 78 geographical factors on sampling efficiency. One appli• GERLOUGH, D. L., and SCHUHL, A., Poisson and Traffic. The cation of this concerns the concept of the economic Eno Foundation for Highway Traffic Control (1955). capacity of the road, the formula for which involves the coefficient of variation of the hourly flows. Values This paper contains two mathematical discussions of the latter are given for some typical roads. of traffic analyses; namely, "Use of Poisson Distribu• tion in Highway Traffic" and 'The Probability Theory Applied to Distribution of Vehicles on Two-Lane GAZIS, D. C, "Optimum Control of a System of Oversaturated Highways." In the first portion, the basic distribution Intersections." Jour. Oper. Res. Sac, Vol. 12, No. 6 is considered and then applied to a number of typical (Nov.-Dec. 1964). traffic problems. The results of the second lead to a The problem of optimizing the control of two over- closer agreement between theory and observations than saturated intersections is solved by semigraphical has been obtained heretofore (e.g., the probability of methods. An analytical formulation of the method a spacing larger than x, probability that an interval using Pontryagin's control theory is also given. It is taken at random contains no vehicles, but is bounded concluded, however, that it is not clear that the control by a vehicle on one side, etc.) theory presented could be useful for a system of more than a few intersections. Particularly, some experi• GERLOUGH, D. L., and WAGNER, F. A., "Improved Criteria for mentation is still needed to establish the feasibility Designing and Timing Traffic Signal Systems." Final of the proposed method in the case of the single Report on NCHRP Project 3-5, Planning Research Corp. intersection. (Mar. 1964). Before the formulation of a model to study traffic GAZIS, D. C, and POTTS, R. B., "The Oversaturated Inter• at individual intersections under laboratory conditions section." International Business Machines Corp. was undertaken, all known past and present research The situation examined in this paper is that of two having a bearing on the subject was reviewed. As a competing demands which exceed the capacity of the result, a comprehensive bibliography of 282 entries intersections. Therefore, for the given condition was prepared and abstracts of the most significant queues are formed and maintained during this period papers (28 entries) are presented along with the bibli• of flow (oversaturation). A method (see Gazis, p. 8) ography in an appendix to this report. The model is presented for optimizing the control of an oversatu• developed for the computer considers in detail the be• rated intersection by a traffic signal to produce a havior of each vehicle in the system (i.e., micro• reduction in delays. scopic). Numerous graphs of vehicular behavior are presented, together with flow charts of the various computational subroutines contained in the model. GERLOUGH, D. L., "Some Problems in Intersection Traffic Future plans include the investigation of various mea• Control." Theory of Traffic Flow, Robert Herman (Edi• sures of effectiveness for intersection control, study tor), Elsevier (1961). of the effectiveness of existing control techniques, and This paper examines some of the problems under• description and testing of new traffic signal control lying the control of traffic at intersections, the existing techniques. intersection control systems, and the areas in which further theoretical study and equipment improvement GILBERT, K., "Evaluation of the Six-Minute Sample Count are required, and presents a progress report on the Procedure." Traffic Eng., pp. 17-20 (Nov. 1962). attack on one of the problems. The discussion is in the terminology and methods of analysis used in This paper describes the 6-min sample count test connection with automatic control systems. It is procedure and presents the results. The test had the pointed out that existing traffic control systems at goals of (a) determining the accuracy of the 6-min intersections are largely open-loop in nature (i.e., sample count procedure over a wide range of volumes, minimum feedback) and that to achieve the greatest and (b) preparing data in useful form as a tool for efficiency techniques must be developed for measuring selecting applications and evaluating results of the and controlling (an agreed-on figure of merit) on a 6-mln count procedure. This count procedure is a closed-loop basis. Further interim solutions to platoon method of estimating existing traffic volumes by taking problems in the form of mathematical representations a 10 percent sample manual count each hour over the of platoons have been proposed. desired counting period. GERLOUGH, D. L., and CAPELLE, D. G. (Editors), "An Intro• GRACE, M. J., and POTTS, R. B., "A Theory of the Diffusion of duction to Traffic Flow Theory." HRB Spec. Report 79 Traffic Platoons." Jour. Oper. Res. Soc, Vol. 12, No. 2, (1964). pp. 255-275 (Mar.-Apr. 1964). This publication is an attempt to consolidate recent This paper presents a theoretical study of the dif• contributions to the theory of traffic flow and present fusion of a traffic platoon as it travels down a road. the material in a related manner with a consistent It is assumed In the mathematical model that the notation. It is noted that many of the theoretical speeds of the vehicles in the platoon are distributed descriptions presented in this paper have not been normally. The parameters of this normal distribution completely validated and verification or refinement is are expressed in terms of a measure of the spreading necessary before the theories can become useful ana• of the platoon (i.e., diffusion constant). The problem lytic tools. Of particular interest to this project is of coordinating two successive traffic lights is solved Chapter Three, entitled "Queuing Theory Approaches." for a number of assumed initial conditions. In the 79 application of the model to the problem of the coordi• GREfcNsmElDS, B. D., and WEIDA, F. M., .Statistics witli Ap• nation of two successive traffic lights, the initial den• plications to Higliway Traffic Analyses. The Eno Foun• sity distribution function was chosen as a rectangular dation for Highway Traffic Control (1952). or trapezoidal pulse on the basis of experimental results. Some of the important limitations of the This book presents a methodical discussion of some model as applied to practice are (a) the theory is Statistical theories and their application in the analysis limited to traffic of medium volume; (b) in the case of traffic data. It is considered by the authors as an of three or more lights it is not clear whether the introduction to the subject. The first four chapters model can be used from signal to signal, or from first explain the mathematics as a tool, and the final chap• to last signal; (c) right or left turning has not been ter shows its application. considered; and (d) no effects of amber phase have been considered. GRIMSDAIX, R. L., MATHERS, R. W., and SUMNER, F. H., "An Investigation of Computer-Controlled Traffic Signals by GRAHAM, E. F., and CHENU, D. C, "A Study of Unrestricted Simulation." Proc. In.it. Civil Eng., Vol. 25, pp. 183-191, Platoon Movements of Traffic." TrafTic Eng. Vol. 32, Paper 6645 (1963). No. 7, pp. 11-13 (Apr. 1962). This paper describes some experiments in computer- This study was performed at a site on US 40 be• controlled traffic signals contained In a particular road tween San Francisco and Sacramento, by the Cali• network. The network and the control philosophies fornia Division of Highways, in cooperation with the were simulated by the Mercury digital computer at Bureau of Public Roads. The objective was to deter• Manchester University. The object of the experiments was to investigate some methods of centralized com• mine the amount of dispersion of platoons released puter-control of traffic signals and in particular the from a traffic signal with minimal downstream inter• provision of signals indicating the best routes between ference. The study concluded that the traffic remained points in the network. Results mdlcated that simple in fairly well-defined platoons for distances of at least fixed-cycle control was the least efficient, whereas 1 mile beyond the rural, isolated, signalized inter• the most efficient control doctrine Incorporated routmg section. control combined with a form of restricted entry. Further discussions on practical difficulties point out GREENBERG, H., and DAOU, A., "The Control of Traffic Flow that an extensive network of measuring devices and to Increase the Flow." Jour. Oper. Res. Soc, Vol. 8, No. 4, communication lines Is required to place the traffic pp. 524-532 (1960). signals of the network under the control of a central computer. Also, the basic measuring devices (vehicle An operational study of tunnel traffic is presented. presence and vehicle flow counters), would have to Data of flow and density at the bottleneck are fitted be placed at selected points along the lane to deter• to a fluid model description of the flow. The control mine the number of vehicles in each lane. The authors of the input traffic by platooning is shown to eliminate suggest that a number of checks could be used to shock waves and permit higher flows. Experimental correct some of the errors that would undoubtedly results are shown to justify the theory and methods occur. presented. GREENSHIELDS, B. D., SCHAPIRO, D., and ERICKSEN, E. L., HAIGHT, F. A.. Mathematical Theories of Traffic Flow. "Traffic Performance at Urban Street Intersections." Tech. Academic Press (1963). Rep. No. I, Yale Bur. of Highway Traffic (1947). This book attempts to justify the theory of traffic This report studies the traffic movements of individ• flow as a part of applied mathematics. Particularly, ual vehicles at both signalized and unslgnalized urban the author attempts to bring out the fundamental intersections. The data were acquired by time-lapse relationship between traffic flow theory and the photography. Hence, a complete record of events classical subjects of queuing theory, stochastic pro• that occurred within the field of view was recorded cesses, and mathematical probability. Although the and In some Instances correlated to the particular terminology of roads and vehicles Is employed, vehicular movements (e.g., comparison of reaction many parts of the book have wider application. time between successive vehicles, showing the effect of the intensity of pedestrian traffic.) Further, since HEWTON, J. T., "The Metropolitan Toronto Automatic Traffic it was possible to distinguish between vehicle classifi• Control System " Traffic Engineering Dept., Municipality cations, a distinction in acceleration and deceleration of Metropolitan Toronto. profiles was made for trucks, buses, and passenger cars. A major effort was made to record starting This report describes Metropolitan Toronto's auto• reaction times to signal changes and between succes• matic traffic control system as proposed by the Traffic sive vehicles at a number of intersections. Although Research Corporation (see Casclato and Cass). A the emphasis of the study is on the transients as• fairly detailed description of the components (com• sociated with the Intersection (e.g., acceleration, de• puter, peripheral equipment, detectors, signal modi• celeration, and reactions), measurements were made fication unit, communications hardware, monitor and during the steady-state condition (i.e., car following). public display units) Is included. Detailed discussions Graphs of time and distance clearances versus speed of the installation procedure and the practical con• are presented. It should be noted that this study was siderations are given The breakdown of the costs is initiated in 1944 and care should be exercised in apply• for a complete system comprising 1,000 signalized ing certain of the empirical, numerical results. Intersections and 2,000 vehicle detectors, although 80 Toronto presently has only 600 signals. A portion is order to evaluate the predictive accuracy of the ex• devoted to explanations and diagrams of the compu• ponential system. tational procedures used for various modes of control. KELL, J. H., "Analyzing Vehicular Delay at Intersections "Highway Capacity Manual—1965." HRB Spec. Report 87 Through Simulation." HRB Bull. 356, pp. 28-39 (1965). (Jan. 1962). The combined efforts of many organizations and This paper describes the development of a model individuals applied in a number of locations for many for the simulation of an intersection of two two-lsuie years have resulted in a great mass of field observa• bi-directional streets, with stop signs controlling one tions. As a consequence of such data and subsequent street. The studies made to obtain adequate mathe• analyses, this manual presents the capacities of rural matical distributions describing traffic behavior are highways with uninterrupted flow, the capacities of discussed. Also presented are the simulation results intersections at grade, weaving intersections, grade along with the formulated relationships between vehic• separations, and ramps, and the relation of hourly to ular delay and approach volumes and turning move• annual average traffic volumes. This document is ments. meant to be a practical guide by which the engineer can design a highway or revamp an old one "with the assurance that the resulting capacity will be as calcu• KELL, J. H., "Intersection Delay Obtained by Simulating Traf• lated." One chapter is devoted to the definitions of fic on a Computer." Highway Research Record No. 15, numerous terms which are necessary and fundamental pp. 73-97 (1963). to the particulars which follow. The intersection model used for the simulation re• sults presented in this paper is an orthogonal inter• section of two, two-lane, two-way streets. The inter• HiLLiER, J. A., "A Review of Developments in Area Traffic section operation has been described for both stop- Control." Proc. First Con/, of the Australian Road Re• sign and signal control. The results (total delay) are search Board, Vol. 1, pp. 416-429 (1962). presented graphically for the stop-sign and fixed-time This paper describes some of the more important signal for various conditions (e.g., volumes, signal existing forms of coordinated area traffic control splits, etc.) (automatic diversion schemes and large-scale linking of signals). Also included is a description of a number KELL, J. H., "Results of Computer Simulation Studies as Re• of proposals which have been made for future de• lated to Traffic Signal Operation." Paper presented at 33rd velopment and the research currently being con• Ann. Meeting, Inst, of Traffic Engineers, Toronto ducted at the Road Research Laboratory. (Aug. 1963). This paper describes the IBM 7090 computer pro• HOEL, P. G., Introduction to Mathematical Statistics, 3rd Ed. gram designed to simulate traffic at an intersection Wiley (1962). controlled by traffic signals. The form of the signal This book considers the theory and application of control may be pre-timed, semi-actuated, or full- statistics simultaneously, although throughout the actuated. The results obtained from the simulation text the emphasis is on the theory. In terms of solv• of the pre-timed signals only, are presented in great ing problems in statistics, this book emphasizes the detail in the form of graphs (e.g., total delay vs vol• selection of a mathematical model and the conclusions ume for various cycle lengths and splits, etc.) It drawn from the model to solve the proposed problem. should be noted that the emphasis of this paper is However, no details are given as to the tests for the on the results of the simulation, with 25 pages de• reasonableness of the model. voted to graphical presentation. HOLT, C. C, MODIGLIANI, F., MUTH, J. F., and SIMON, H. A., LEISCH, J. E., "Design Capacity Charts for Signalized Street Planning Production, Inventories and Work Force. Pren• and Highway Intersections." Pub. Roads, Vol. 26, No. 6. tice-Hall (1960). This paper presents a method of graphic analysis This book undertakes to describe some decision• based on Part V of the Highway Capacity Manual making mathematical techniques and how they may (1950 edition), which describes a method of analysis be applied to managerial decisions in the operation for the calculation of capacity at signalized inter• of a factory warehouse system. Although the methods sections under various conditions. The design capacity reported were developed in the context of a factory charts are presented with typical examples for various supplying a warehouse system, they are applicable to types of signal-controlled intersections on two-way the corresponding decision problems in the operation streets, one-way streets, and expressways. of military and other governmental organizations. Moreover, the basic mathematical tools can be LITTLE, J. D. C, MARTIN, B. V., and MORGAN, J. T., "Syn• adapted to use in other fields. Of particular interest chronizing Traffic Signals for Maximal Bandwidth." Dept. is Chapter 14, entitled "Forecasting Sales of Individual of Civil Engineering, MIT (Mar. 1964). Products by Exponentially Weighted Moving Aver• ages," which includes details on the methods of fore• This paper contains a description of an IBM 1620 casting (including modifications to take account of computer program (a listing and operating instruc• seasonal and trend effects), selection of weights and tions are included) developed for the solution of two initial value, and tests of the forecasting methods in particular traffic problems. The first is: Given an arbitrary number of signals along a street, a common trol, and particularly its dependence on sensory de• cycle length, the green and red times for each signal, vices (i.e., detectors and human observations). and specified vehicle speeds in each direction between adjacent signals, synchronize the signals to produce MILLER, A. J., "Settings for Fixed-Cycle Traffic Signals." Oper. bandwidths that are equal in each direction and as Res. Quart. (Dec. 1963). large as possible. The second is to adjust the synchro• nization to increase one bandwidth to some specified This paper presents the full mathematical details feasible value and maintain the others as large as of the derivation of a formula to represent the aver• possible. The definition of bandwidth is given as "that age delay to vehicles at junctions controlled by fixed- portion of a signal cycle for which it is possible for a cycle traffic signals. The delays predicted are close to vehicle starting at one end of a street and traveling those observed in practice. The delay formula is used at preassigned speeds to go to the other end without to derive optimum signal settings. stopping for a red light." NATIONAL JOINT COMMITTEE ON UNIFORM TRAFFIC CONTROL MATSON, T. M., SMITH, W. S., and HURD, F. W., Traffic Engi• DEVICES, Manual on Uniform Traffic Control Devices for neering. McGraw-Hill (1955). Streets and Highways. U. S. Dept. of Commerce (June 1961). This book attempts to explain highway traffic phe• nomena by simple and elementary analyses. The book This manual sets forth the basic principles that is divided into five sections entitled, "Characteristics," govern the design and use of traffic control devices. "Regulations," "Control Devices and Aids," "Design," These principles appear throughout the text in dis• and "Administration and Planning." Of particular in• cussions of the devices to which they apply. The terest is the discussion of vehicle characteristics and standards apply to any and all streets. Where a traffic signals. device is intended for limited application only, or for a specific system, the text specifies the restrictions on its use. Although the manual describes the appli• MILLER, A. J., "A Computer Control System for Traffic Net• cation of the various devices, it is not intended as a works." Second Internal. Symposium on Theory of Road substitute for engineering judgment. Both engineering Traffic Flow, Univ. of Birmingham (England) (June judgment and imaginative application are essential to 1963). true uniformity. This paper describes a method of controlling traffic signals employing the minimum-delay criterion. The OLIVER, R. M., "Travel Times Through Shock Waves." Oper. implementation requires a digital computer fed Res. Quart., Vol. 15, No. 2 (June 1964). information from strategically located detectors. With the control system described, the computer inter• This paper formulates the principle of conservation rogates all the intersections in the network within a of matter with an integral equation which expresses predetermined time interval to make the decision to travel times in the traffic stream. A particular situa• have the current signal state unchanged for some tion is presented whereby the flow rates into the integral multiple of the time interval, or change the bottleneck (which are time dependent) temporarily signals immediately. The decisions are based on exceed the capacity of the bottleneck. Expressions are measurements and/or estimates of queue lengths, presented for queue sizes, location and velocity of departure and arrival rates, phase duration, etc. De• shock waves, and delays to vehicles in the traffic tectors are proposed at stop-line and midblock loca• stream. tions for each approach. The emphasis is on the individual intersection, although there is a discussion Data Pro- of network considerations. Also included are com• "San Jose Traffic Control Study, Initial Report.' ments on exponentially weighted moving averages (as cessing Div., IBM, Kingston, N. Y. a prediction technique), fixed-time synchronization, This report contains a description of a particular quantity control (limiting queue lengths), and route digital-computer control system, including details of control. the management and hardware necessary for its im• plementation. Computational procedures of various subroutines are presented, with a functional descrip• MILLER, A. J., "Computers in the Analysis and Control of tion of the system's operation and specifications. The Traffic." Dept. of Transportation, Univ. of Birmingham study will begin with known methods of control in (England). Paper prepared for a conference on Com• Phase I and work toward implementing improved puters in Civil Engineering. methods of arterial control; plans for Phase II include This paper attempts to justify the use of computers the more difficult techniques for grid control. in the control of traffic. The justification is sought by finding control strategies which are superior to SCHENLER, W. W., and MICHAEL, H. L., "A Sufficiency Rating those available with existing controllers. That is to Method for Urban Intersections." Civil Engineering Dept., say, strategies that could appreciably reduce delays Purdue Univ. (July 1963). over what could optimally be expected from conven• tional techniques and equipment. The paper briefly This paper recognizes that the rating of urban high• discusses various forms of computer control but only ways is much more complex than the rating of rural considers timing control in detail. The isolated inter• roads. In particular, any evaluation of a major urban section is developed, then the network case. Also street must of necessity include an evaluation of the pointed out are the limitations of such machine con• intersections on that street. This report briefly de- 82 scribes the development of a sufficiency rating method within the network can be decreased by up to 10 for such intersections based on engineering procedures. percent during peak periods and up to 20 percent Two factors were considered to influence the ability of during off-peak periods. an intersection to serve traffic; namely, physical and traffic factors. The physical rating includes such fac• WALKER, H. M., and LEV, J., Statistical Inference. Holt, Rine- tors as surface condition, ridability, and skid resist• hart and Winston (1963). ance, as is conventional. Also considered were inter• section geometries, curb radius for right-turning This book on statistics does not presuppose any vehicles, visual restrictions, and lighting. The traffic college training In mathematics, hence does not present rating used average delay per vehicle as a measure mathematical derivations of formulas. Therefore, all of user satisfaction with the service provided. This concepts are introduced by the intuitive approach. Of traffic rating is determined for each approach to the particular Interest to the project Is Chapter 10, en• particular intersection being investigated. titled "Linear Regression and Correlation," in which the authors present the results in a form suitable for SCHWAR, I. F., and PUY-HUARTE, J., "Statistical Methods in machine computations. Traffic Engineering." Eng. Exper. Station, The Ohio State University (Sept. 1962). WEBSTER, F. V., "Traffic Signal Settings." Road Research Tech. This manual is not intended to be a textbook on Paper No. 39, HMS Office (1958). statistics, as only a minimum of theory is presented. This paper presents results of research conducted by Emphasis is on the typical examples found in traffic the British Road Research Laboratory into the delays engineering, chosen to cover those statistical methods to vehicles at fixed-time traffic signals. Also included most commonly used in the field. is the formula for the optimum settings of such signals. The methods developed can be applied to both fixed- "Use of Electronics in Traffic Control." Theme V, Worid time and vehicle-actuated controlled intersections with Traffic Eng. Conf., combining 31st Ann. Meeting, Inst, some modifications. An expression is given for the of Traffic Eng. and International Sessions in Traffic En• average delay per vehicle in terms of both theoretical gineering (Aug. 1961). and empirical results. It is from this basic equation that the optimization concepts are developed and Theme V presents seven papers from all parts of the world concerning the use of electronics in traffic con• tables and graphs are presented of various parameters. trol. Topics covered are vehicle guidance, simulation, computer control of traffic signals, electronic equip• WILDERMUTH, B. R., "Average Vehicle Headways at Signalized ment, etc. Intersections." Traffic Eng., pp. 14-16 (Nov. 1962). This paper presents the results of a study made to WAGNER, F. A., RUDDEN, J. B., and GERLOUGH, D. L., "Final determine the average vehicle headways at signalized Report, Study of the Traffic Signal System In a Portion of intersections under different conditions. The factors the District of Columbia. Volume I. Study Techniques which were considered to influence headways were and Results." Thompson Ramo Wooldridge, Inc. (Apr. length of phase, amount of heavy vehicles, amount of 1963). turning traffic, and direction of traffic movement. The The purpose of the study was to "simulate signalized results indicate headways in agreement with the Higli- thoroughfares in the study area by means of Monte way Capacity Manual for short green phases. Head• Carlo techniques, utilizing mathematical models on a ways were found to be below 2.0 sec for phases high-speed digital computer to determine the optimum between 35 and 45 sec (note that 2.0 sec represents signal timing plan which will assume total delay as a 1,800 vph of green, approximating freeway measure• measure of effectiveness." A macroscopic model of ments). Details of the analysis are presented. the network was formulated, and various traffic signal timing plans were tested by simulation runs on a YARDENI, L. A., "Vehicular Traffic Control: A Time-Space large-scale digital computer. The model was scanned Design Model." IBM Corp. (Nov. 1964). or sampled at 5-sec intervals. The distribution of the number of vehicles arriving during each 5-sec interval This paper describes a computer program which can was assumed to be Poisson. A detailed analysis of be used for the design of traffic signal settings to pro• the actual behavior of platoons on the street network duce progressions for fixed-time control. The program under study was carried out. Numerous graphs and uses least-squares and minimax fit models to derive tables presenting platoon behavior are included. Signal through-bands for given volume requirements and timing plans have been found which suggest that delay within the given limits of speed and cycle times. Published reports of the • 'f S-^Ss NATIONAL COOPERATIVE HIGHWAY RESEARCH PROGRAM J t ^^W* are available from: Highway Research Board National Academy of Sciences 2101 Constitution Avenue Washington, D.C. 20418 NCHRP Report No. Title —* A Critical Review of Literature Treating Methods of Identifying Aggregates Subject to Destructive Volume Change When Frozen in Concrete and a Proposed Program of Research—Intermediate Report (Project 4-3(2)) 81pp. $1.80 1 Evaluation of Methods of Replacement of Deteriorated Concrete in Structures (Project 6-8) 56 pp. $2.80 2 An Introduction to Guidelines for Satellite Studies of Pavement Performance (Project 1-1) 19 pp. $1.80 2A Guidelines for Satellite Studies of Pavement Performance 85 pp.-l- 9 figs., 26 tables, 4 app. $3.00 3 Improved Criteria for Traffic Signals at Individual Intersections—Interim Report (Project 3-5) 36 pp. $1.60 4 Non-Chemical Methods of Snow and Ice Control on Highway Structures (Project 6-2) 74 pp. $3.20 5 Effects of Different Methods of Stockpiling Aggregates—Interim Report (Project 10-3) 48 pp. $2.00 6 Means of Locating and Communicating with Disabled Vehicles—Interim Report (Project 3-4) 56 pp. $3.20 7 Comparison of Different Methods of Measuring Pavement Condition—Interim Report (Project 1-2) 29 pp. $1.80 8 Synthetic Aggregates for Highway Construction (Project 4-4) 13 pp. $1.00 9 Traffic Surveillance and Means of Communicating with Drivers—Interim Report (Project 3-2) 28 pp. $1.60 10 Theoretical Analysis of Structural Behavior of Road Test Flexible Pavements (Project 1-4) 31 pp $2.80 11 Effect of Control Devices on Traffic Operations—Interim Report (Project 3-6) 107 pp. $5.80 12 Identification of Aggregates Causing Poor Concrete Performance When Frozen—Interim Report (Project 4-3(1)) 47 pp. $3.00 13 Running Cost of Motor Vehicles as Affected by Highway Design—Interim Report (Project 2-5) 43 pp. $2.80 14 Density and Moisture Content Measurements by Nuclear Methods—Interim Report (Project 10-5) 32 pp. $3.00 15 Identification of Concrete Aggregates Exhibiting Frost Susceptibility—Interim Report (Project 4-3(2)) 66 pp. $4.00 16 Protective Coatings to Prevent Deterioration of Concrete by Deicing Chemicals (Project 6-3) 21 pp. $1.60 17 Development of Guidelines for Practical and Realistic Construction Specifications (Project 10-1) 109 pp. $6.00 18 Community Consequences of Highway Improvement (Project 2-2) 37 pp. $2.80 19 Economical and Effective Deicing Agents for Use on Highway Structures (Project 6-1) 19 pp. $1.20 20 Economic Study of Roadway Lighting (Project 5-4) 77 pp. $3.20 21 Detecting Variations in Load-Carrying Capacity of Flexible Pavements (Project 1-5) 30 pp. $1.40 22 Factors Influencing Flexible Pavement Performance (Project 1-3(2)) 69 pp. $2.60 23 Methods for Reducing Corrosion of Reinforcing Steel (Project 6-4) 22 pp. $i.40 24 Urban Travel Patterns for Airports, Shopping Centers, and Industrial Plants (Project 7-1) 116 pp. $5.20 25 Potential Uses of Sonic and Ultrasonic Devices in Highway Construction (Project 10-7) 48 pp. $2.00 26 Development of Uniform Procedures for Establishing Construction Equipment Rental Rates (Project 13-1) 33 pp. $1.60 27 Physical Factors Influencing Resistance of Concrete to Deicing Agents (Project 6-5^ 41 pp. $2.00 28 Surveillance Methods and Ways and Means of Communicating with Drivers (Project 3-2) 66 pp. $2.60 29 Digital-Computer-Controlled Traffic Signal System for a Small City (Project 3-2) 82 pp. $4.00 •Highway Research Board Special Report 80. THE NATIONAL ACADEMY OF SCIENCES is a private, honorary organiza- tion of more than 700 scientists and engineers elected on the basis of outstanding contributions to knowledge. Established by a Congressional Act of Incorporation signed by President Abraham Lincoln on March 3, 1863, and supported by private and public funds, the Academy works to further science and its use for the general welfare by bringing together the most qualified individuals to deal with scientific and technological problems of broad significance. Under the terms of its Congressional charter, the Academy is also called upon to act as an official—yet independent—adviser to the Federal Government in any matter of science and technology. This provision accounts for the close ties that have always existed between the Academy and the Government, although the Academy is not a governmental agency and its activities are not limited to those on behalf of the Government. THE NATIONAL ACADEMY OF ENGINEERING was established on December 5, 1964. On that date the Council of the National Academy of Sciences, under the authority of its Act of Incorporation, adopted Articles of Organization bringing the National Academy of Engineering into being, independent and autonomous in its organization and the election of its members, and closely coordinated with the National Academy of Sciences in its advisory activities. The two Academies join in the furtherance of science and engineering and share the responsibility of advising the Federal Government, upon request, on any subject of science or technology. THE NATIONAL RESEARCH COUNCIL was organized as an agency of the National Academy of Sciences in 1916, at the request of President Wilson, to enable the broad community of U. S. scientists and engineers to associate their efforts with the limited membership of the Academy in service to science and the nation. Its members, who receive their appointments from the President of the National Academy of Sciences, are drawn from academic, industrial and government organizations throughout the country. The National Research Council serves both Academies in the discharge of their responsibilities. Supported by private and public contributions, grants, and contracts, and volun• tary contributions of time and effort by several thousand of the nation's leading scientists and engineers, the Academies and their Research Council thus work to serve the national interest, to foster the sound development of science and engineering, and to promote their effective application for the benefit of society. THE DIVISION OF ENGINEERING is one of the eight major Divisions into which the National Research Council is organized for the conduct of its work. Its membership includes representatives of the nation's leading technical societies as well as a number of members-at-large. Its Chairman is appointed by the Council of the Academy of Sciences upon nomination by the Council of the Academy of Engineering. THE HIGHWAY RESEARCH BOARD, organized November 11, 1920, as an agency of the Division of Engineering, is a cooperative organization of the high• way technologists of America operating under the auspices of the National Research Council and with the support of the several highway departments, the Bureau of Public Roads, and many other organizations interested in the development of highway transportation. The purposes of the Board are to encourage research and to provide a national clearinghouse and correlation service for research activities and information on highway administration and technology.