SOFTWARE DEVELOPMENT FOR MULTIPATH ROUTE ASSIGNMENT TECHNIQUE

A DISSERTATION Submitted in partial fulfillment of the requirements for the award of the degree of MASTER OF TECHNOLOGY in CIVIL ENGINEERING (With Specialization in Computer Aided Design)

By RANJEET KUMAR

•

DEPARTMENT OF CIVIL ENGINEERING INDIAN INSTITUTE OF TECHNOLOGY ROORKEE ROORKEE - 247 667 (INDIA) JUNE, 2006 CANDIDATE'S DECLARATION

I hereby declare that the work which is presented in this dissertation titled

"SOFTWARE DEVELOPMENT FOR MULTIPATH ROUTE ASSIGNMENT

TECHNIQUE " being submitted by me in partial fulfillment of the requirements for the award of Master of Technology in Civil Engineering with the specialization in

Computer Aided Design in Civil Engineering at the I.I.T. Roorkee is a authentic work carried by me under supervision of Dr. PRAVEEN KUMAR, Associate Professor in

Transportation Engineering, I.I.T. Roorkee.

r \4■-tw-c4.- (RANJEET KUMAR) M.Tech. (CAD)

Place: Roorkee Department of Civil Engineering

Date: 2C IsCia6 Roorkee

CERTIFICATE

This is to certify that the above declaration made by candidate is correct to the best of my knowledge.

(Dr. PRAVEEN KUMAR) Associate Professor Transportation Engineering Place: Roorkee Civil Engineering Department Date: 246416.6 Roorkee ACKNOWLEDGEMENT

I wish to express my most sincere appreciation and deep sense of gratitude to Dr. Praveen Kumar, Associate professor in Transportation Engineering, I.I.T. Roorkee, Roorkee for the fruitful discussions, kind help, continued encouragement and invaluable guidance enabling me to bring this dissertation report in the present form. I am extremely grateful to all of my friends, colleagues and well-wishers for their candid help, meaningful suggestions and persistent encouragement given to me from time to time, which went a long way in bringing this work to its present state.

&xi ee 14tAiiteOtie (Ranjeet Kumar)

ii ABSTRACT

The main objective of this dissertation report is to present an overview of the software development of multipath route assignment technique. At first four stage transportation planning is discussed. The last stage is route assignment. Mainly there are four techniques for route assignment i.e. all-or-nothing assignment, capacity restraint technique, multipath-technique, and diversion curves technique. The choice of routes in the development of transportation planning depends upon certain parameters like journey time, distance, cost, comfort, and safety. In this report, I have to discuss about capacity restraint multipath route assignment technique and to develop software for route assignment by this technique. In all the above four techniques, Multipath route assignment technique conforms to the real-life traffic situation and also is accurate. The software developed for route assignment is in visual basic. The software is user friendly and any one can use easily without any difficulty. The software gives output in both text and graphical form. It gives result for both multipath route assignment and capacity restrained multipath route assignment technique. In this software iterations are stopped after establishing equilibrium between traffic entering at origin equal to traffic reach at destination. The main aim of capacity restrained multipath route assignment technique is that the volume at any link not greater than the capacity of that link. For this we have to use a factor equal to the ratio of assigned volume to capacity of that link which is greater than 1. The link is used as redundant link, which has factor greater than 1 and after that new volume is assigned to each link by dividing the assigned volume to factor calculated. Again multipath route assignment technique is applied to calculate the final volume to each link. In this technique, attempts have been done to overcome the drawbacks of "all-or-nothing assignment" and "capacity restraint technique".

iii CONTENTS

S.N. TOPIC PAGE NO.

CERTIFICATE ACKNOWLEDGEMENT ii ABSTRACT iii LIST OF FIGURES vi LIST OF TABLES viii 1. INTRODUCTION 1-3 1.1 GENERAL 1 1.2 NEED OF STUDY 1 1.3 OBJECTIVE OF THE STUDY 2 1.4 THESSIS ORGANIZATION 3 2. LITERATURE REVIEW 4-13 2.1 GENERAL 4 2.2 HISTORICAL CONTEXT 4 2.3 CASE STUDIES CONDUCTED ABROAD 5 2.4 CASE STUDIES CONDUCTED IN INDIA 11 3. TRANSPORTATION PLANNING 14-22 3.1 GENERAL 14 3.2 TRAVEL DEMAND FORECAST 15 3.3 SEQUENTIAL DEMAND FORECASTING MODELS 15 3.3.1 Trip Generation 17 3.3.2 Trip Distribution 19 3.3.3 Modal Choice 20 3.3.4 Route Assignment 21 4. ROUTE ASSIGNMENT 23-38 4.1 GENERAL 23 4.2 GENERAL PRINCIPLE 23 4.3 ROUTE ASSIGNMENT TECHNIQUE 24

iv S.N. TOPIC PAGENO.

4.3.1 All-or-Nothing Assignment 24 4.3.2 Capacity Restraint Technique 26 4.3.3 Multipath Route Assignment 28 4.3.4 Diversion Curves Technique 32 4.4 ELEMENTS OF TRAFFIC ASSIGNMENT 34 4.5 PRACTICAL PROBLEMS IN TRAFFIC ASSIGNMENT 37 5. SOFTWARE DEVELOPMENT 39-56 5.1 GENERAL 39 5.2 SOFTWARE REVIEW 39 5.3 SOFTWARE PRINCIPLE 40 5.4 SOFTWARE DEVELOPMENT PROCEDURE 41 5.5 FLOW CHART 44 5.6 MODULE OF SOFTWARE 49 5.7 FEATURES OF SOFTWARE 56 6. VALIDATION OF THE SOFTWARE 57-96 6.1 GENERAL 57 6.2 DATA FOR VALIDATION 57 6.3 ANALYSIS OF DATA 58 6.3.1 Manual Analysis 58 6.3.2 Computer Analysis 80 6.4 COMPARISION OF RESULTS 96 7. CONCLUSION AND RECOMMENDATION 97 7.1 CONCLUSIONS 97 7.2 RECOMMENDATION 97 REFERENCES 98-100 APPENDIX 101-126 LIST OF FIGURES

F.N. TITLES PAGE NO.

3.1 THE SEQUENTIAL DEMAND FORECASTING PROCESS 16 3.2 ESTIMATION OF TRIP DISTRIBUTION 20 3.3 MODAL CHOICE MODEL 21 3.4 FOUR STAGE TRANSPORTATION PLANNING PROCESS 22 5.1 SCREEN PRINT OF GENERAL MODULE 49 5.2 SCREEN PRINT OF INPUT DATA 1 MODULE 50 5.3 SCREEN PRINT OF INPUT DATA 2 MODULE 51 5.4 SCREEN PRINT OF INPUT DATA 3 MODULE 52 5.5 SCREEN PRINT OF INPUT DATA 4 MODULE 53 5.6 SCREEN PRINT OF INPUT DATA 5 MODULE 54 5.7 SCREEN PRINT OF OUTPUT RESULT MODULE 55 6.1 INITIAL ROAD NETWORK AND THEIR DISTANCE 57 6.2 SHORTEST PATH DISTANCE FOR EACH NODE TO DESTINATION 59 6.3 CALCULATED TRAFFIC VOLUMES AT EACH LINK (15 ITERATION) 69 6.4 READJUSTED TRAFFIC VOLUMES AT EACH LINK 70 6.5 ROAD NETWORK AND THEIR DISTANCE 71 6.6 FINAL TRAFFIC VOLUMES AT EACH LINK (15 ITERATION) 79 6.7 SCREEN PRINT OF ENTERING NO.OF NODE AND NO.OF LINK 80 6.8 SCREEN PRINT OF ENTERING COORDINATE OF EACH LINK 81 6.9 SCREEN PRINT OF INPUT OF TRAVEL TIME FOR EACH LINK 82 6.10 SCREEN PRINT OF INPUT OF LINK CAPACITY 83 6.11 SCREEN PRINT OF INPUT OF TRAFFIC FLOW FROM ORIGIN DESTINATION 84 6.12 SCREEN PRINT OF RESULT MODULE 85 6.13 SCREEN PRINT OF OUTPUT OF SHORTEST PATH BY MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 86

vi F.N. TITLES PAGE NO.

6.14 SCREEN PRINT OF OUTPUT OF CALCULATED DISTANCE OF EACH LINK BY MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 87 6.15 SCREEN PRINT OF OUTPUT OF PROBABILITY MATRIX BY MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 88 6.16 SCREEN PRINT OF OUTPUT OF TRAFFIC VOLUME BY MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 89 . 6.17 SCREEN PRINT OF PICTORIAL VIEW OF OUTPUT BY MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 90 6.18 SCREEN PRINT OF OUTPUT OF SHORTEST PATH BY CAPACITY RESTRAINT ROUTE ASSIGNMENT MULTIPATH TECHNIQUE 91 6.19 SCREEN PRINT OF OUTPUT OF CALCULATED DISTANCE OF EACH LINK BY CAPACITY RESTRAINT MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 92 6.20 SCREEN PRINT OF OUTPUT OF PROBABILITY MATRIX BY CAPACITY RESTRAINT MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 93 6.21 SCREEN PRINT OF OUTPUT OF TRAFFIC VOLUME BY CAPACITY RESTRAINT MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 94 6.22 SCREEN PRINT OF PICTORIAL VIEW OF OUTPUT BY CAPACITY RESTRAINT MULTIPATH ROUTE ASSIGNMENT TECHNIQUE 95

vii LIST OF TABLES

T.N. TITLE PAGE NO.

5.1 SOFTWARE PACKAGES AND DEVELOPER 40 6.1 ROAD NETWORK DATA 58 6.2 TRAFFIC VOLUME CALCULATED DATA 96

viii CHAPTER- 1 INTRODUCTION 1.1 GENERAL

Transportation contributes to the economic, industrial, social and cultural development of any country. Transportation is vital for the economic development of any region since every commodity produced whether it is food, clothing, industrial products or medicine needs transport at all stages from production to distribution. It is not only the key infrastructural input for the growth process but also plays a significant role in promoting national integration, which is particularly important in a large country like India. The transport system also plays an important role of promoting the development of the backward regions and integrating them with the mainstream economy by opening them to trade and investment. In a liberalized set up, an efficient transport network becomes all the more important in order to increase productivity and enhancing the competitive efficiency of the economy in the world market. In the production stage, transportation is required for carrying raw materials like seeds, manure, coal, steel etc. In the distribution stage, transportation is required from the production centers viz; farms and factories to the marketing centers and later to the retailers and consumers for distribution. The inadequate transportation facilities retard the process of socio-economic development of country. The adequacy of transportation system of a country indicates its economic and social development. In addition, the road system also provides linkages to other modes such as Railways, Airports, Ports and Inland Waterway Transport, and complements the efforts of these modes in meeting the needs of transportation.

1.2 NEED OF THE STUDY The subject matter of transportation planning is to plan a transportation network for efficient, comfortable and safe traffic operations at minimal cost. In most of the metropolitan cities of our country, there is lack of good network systems. The road network, though extensive, remains inadequate in terms of spread, suffers from a number of deficiencies and is unable to handle high traffic

1 density at many places and has poor riding quality in some segments. The main reason for these shortcomings is the inadequacy of funds. Efforts are now underway to address these issues, and improvement in the road network has been accorded a very high priority. This expansion of capacity will have to be accompanied by technological up gradation in many critical areas. The need for new technology acquires greater urgency because the sector had been suffering from slow technological development for a long time. Route selections in the transportation network are based on certain quantitative and qualitative parameters like travel-time, link-volume, link-distance, cost, comfort and safety. A large number of route assignment techniques are available today. But maximum of them suffer from some drawbacks. Multipath route assignment technique is a concept, which is intended to assign traffic to all the routes available in the road network, instead of assigning all the traffic to the shortest route. In the present study attempts have been done to give a compact model for route assignment using multipath technique, where capacity constraints of routes have been incorporated. The main aim of this study is to prepare user-friendly software for route assignment by the above technique, so that route assignment can be made possible for large road networks using this highly iterative technique.

1.3 OBJECTIVES OF THE STUDY The present work was undertaken with the following objectives: 1. To review the studies on route assignment. 2. To define and discuss about four-stage transportation planning. 3. To discuss about route assignment in general. 4. To develop a software for route assignment. 5. To apply and validate the software.

2 1.4 THESIS ORGANIZATION The thesis report has been organized in seven chapters in logical and sequential manner. Chapter 1 introduces about the transportation in India in brief, need of the transportation planning and objective of the study of this thesis. Chapter 2 deals about the review of literature which is presented for different route assignment in different condition in India or abroad. Chapter 3 deals about the transportation planning in detail. This chapter also discusses about the travel demand forecasting and four stage of transportation planning in brief. Chapter 4 deals about the traffic assignment which is the fourth stage of urban transportation planning in detail. This chapter discusses about the different type of traffic assignment in detail. Chapter 5 deals about the methodology of software development. This chapter contains the theory behind the software, flow chart for software developMent, module of developed software. ?;; Chapter 6 deals about the validation of software. For validation of software, it is to use actual data and find out the result manually and by developed software. Then both the results are compared. Chapter 7 deals about the conclusions and recommendation based on the study of this thesis.

3 CHAPTER-2 LITERATURE REVIEW 2.1 GENERAL Traffic assignment estimates the expected flows that the links of the highway network are likely to experience to help anticipate potential capacity problems and to plan accordingly. It requires a behavioral hypothesis of route choice, a method of describing the highway network for computer processing, a way of selecting the appropriate inter-zonal paths, and a way of realistically allocating the inter-zonal volumes on these paths. In this chapter discussion will be about the studies that have been carried out in the field of traffic assignment in India as well as abroad.

2.2 HISTORICAL CONTEXT The origin of traffic assignment can be traced to the 1950s and 1960s, when the majority of urban freeways were constituted in United States cities. First, highway engineers develop diversion-curve model to know how many drivers would be diverted from arterial streets to a proposed freeway in order to make decisions relating to the geometric design and capacity of propoSed urban freeways. This model employs empirically derived curves to compute the percentage of trips that would use the freeway route between two points on some measure of relative impedance between the freeway route and the fastest arterial route between the two points. Maskowitz (1956) carried out a study using California diversion curves. In this model, difference of travel time and travel distance in the two alternative paths to estimate the percentage of trips that use the freeway, was used. In 1964 Bureau of public roads (B.P.R.) developed diversion curves in which they used the ratio of travel times as measure of impedance.

4 2.3 STUDIES CONDUCTED ABROAD Edwards and Robinson (1977) presented a paper on "Multipath assignment calibration for the twin cities". This research is based on Dial's probabilistic multipath traffic assignment algorithm. This research project was undertaken at the University of Minnesota and jointly supported by the twin cities Metropolitan council and the Minnesota highway department to investigate the use of the probabilistic multipath option in UTPS program UROAD. The main objective of this research was to calibrate the probabilistic multipath model using the 1970 highway network for the twin cities together with recorded ground count volumes from the same year and to investigate the sensitivities of the model outputs to changes in input parameters and establish general guidelines for future use of the model in the twin cities metropolitan area.

Peeta (1995) of Purdue University, West Lafayette, U.S.A. and Mahmassani H.S. of The university of Texas at Austin, U.S.A. presented a paper on traffic assignment with name "Multiple user classes Quasi-Real-time Traffic Assignment for online operations: A rolling horizon solution framework". They discussed in this paper that rolling horizon framework addressing the real-time traffic assignment problem, where an ATIS/ATMS controller is assumed to have O-D desires up to the current time interval and short-term and medium-term forecasts of future O-D desires. The assignment problem is solved in quasi-real time for a near term future duration to determine an optimal path assignment scheme for users entering the network in real-time for the short-term roll period. In this paper they discussed two formulations and a solution procedure for the multiple user classes quassi-real time traffic assignment (MUCQRTA) problem, which addresses the real time implementation needs of ATIS. The rolling horizon solution procedure was implemented on a CRAY Y- MP supercomputer. The rolling horizon approach used previously for production inventory control (Wanger, 1977) and in transportation engineering for online demand-responsive traffic signal control (Gartner, 1982, 1983) provided a practical method for addressing the real-time traffic assignment problem.

5 Carlos (2002) presented a paper on "Reversibility of the time-dependent shortest path problem". In this paper he discussed about the problem of fmding the shortest path from an origin to a destination over a network in which the link travel times are time-dependent is of central importance in dynamic traffic assignment (DTA) and many other applications. Time-dependent shortest path problems arise in a variety of applications; e.g., dynamic traffic assignment (DTA), network control, automobile driver guidance, ship routing and airplane dispatching. In the majority of cases one seeks the cheapest (least generalized cost) or quickest (least time) route between an origin and a destination for a given time of departure. This is the "forward" shortest path problem. In some applications, however, e.g., when dispatching airplanes from airports and in DTA versions of the "morning commute problem", one seeks the cheapest or quickest routes for a given arrival time. This is the "backward" shortest path problem. It is shown that an algorithm that solves the forward quickest path problem on a network with first-in-first-out (FIFO) links also solves the backward quickest path problem on the same network.

Nicholas, Joshua and Kyriacos (1996) presented a paper on "A strategy for solving static multiple-optimal-path transit network problems". He discussed in this paper to develop an algorithm and strategy for transit providers to find best alternatives for the user and to demonstrate how a geographic information system (GIS) can be used in the development of a transit advanced traveler information system (TATIS) to meet these needs. The main features of the proposed algorithm are capability of handling multiple mode of transit, to providing path that include walking distances from and to the transit path as well as between transfer points and provision of multiple optimal paths to allow the user flexibility in choosing a path. '

Boyce, Lee, Janson, and Berka (1997) presented a paper on "Dynamic route choice model of large-scale traffic network". In this paper, they discussed about a dynamic user-optimal route choice model for predicting real-time traffic flows for advanced traffic management system (ATMS) and advanced traveler information

6 systems (ATIS). The problem analyzed in this paper is specified route choice behavior (e.g. user-optimal) and time-dependent transportation supply variation. The network equilibrium model is used for traffic assignment. This model was implemented on the Convex-C3880 at the National centre for supercomputing applications (NCSA), University of Illinois at Urbana-Champaign.

Lam, Gao, Chan, and Yang (1999) of Department of Civil & Structural Engineering, The Hong Kong Polytechnic University, Hong Kong Department of Civil Engineering, The University of Science and Technology, Hong Kong presented a paper on "A stochastic user equilibrium assignment model for congested transit networks". In this paper, he presented a model to predict how passengers will choose their optimal routes and estimate the total passenger travel cost in a "congested transit network. The stochastic effects of the passenger's behavior and overcrowd vehicle's arrivals are incorporated in the proposed model. A mathematical programming problem is formulated and equivalent to the SUE assignment problem in congested transit networks. When the in-vehicle link capacity constraints are reached, it is proven that the Lagrange multi-pliers of the mathematical problem give the equilibrium passenger overload delays in the transit network. TRANSEPT (Last and Leak, 1976) was the first model to consider transit vehicle capacity. The model is suitable only for radial networks. De Cea and Fernandez (1993) presented a user equilibrium (UE) assignment model for the transit assignment problem on congested systems, in which the "transit route" and the "effective frequency" were introduced. Wu et al. (1994) proposed an approach to the formulation of the transit UE assignment problem that is considered to be an extension of the nonlinear model (Spiess and Florian, 1989). This was applied to the situation for an asymmetric transit link cost function based on the strategy or hyper-path concept of a general network.

Nielsen (2000) of Centre for Traffic and Transport Research, Department of Planning (IFP), Technical Unhiersity of Denmark (DTU), Denmark presented a paper on "A stochastic transit assignment model considering differences in

7 passenger's utility functions". In this paper, he presented a framework for public traffic assignment that builds on the probit-based model of Sheffi Y. and Powell W.B. (1981). In this model the problems with overlapping routes that occur in many public transport models are to be avoided.

Lam, Member ASCE, and Zhang (2000) presented a paper on "Capacity- Constrained Traffic Assignment in Network with Residual Queues". In this paper, he discussed about the road networks with residual queues using steady state user equilibrium principle. An equivalent mathematical model is proposed for congested networks, particularly when the traffic O-D demands exceeds the capacity of road network. The main aim of this proposed model is the strategic transportation planning, but also taking in to account the effects of residual queues. Therefore, the queuing effect can be incorporated in to the strategic transport model for traffic forecasting. Lam and Yin (2001) of Department of Civil and Structural Engineering, The, Hong Kong Polytechnic University, Hung Hon, Kowloon, Hong Kong Presented a, paper on "An activity-based time-dependent traffic assignment model". In this paper, he proposed a model for a variational inequality for the dynamic user equilibrium activity/route choices. A heuristic solution method is proposed and applied to a numerical example for illustration. hi this paper, he employed the concept of the temporal utility profile of activities to model the activity choice behaviors. He considered his model is simplified travel demand analysis tool for long term strategy planning.

Peeta and Yang (2003) of school of Civil Engg., Purdue University, West Lafayette, USA presented a paper on stability issues for dynamic traffic- assignment. In this paper they discussed the stability issues for operational route guidance control strategies for vehicular traffic networks equipped with advanced information systems and develop a general procedure for the stability analysis of the associated dynamic traffic assignment (DTA) problems. The problem is formulated as a non-linear dynamical system within a feedback control framework.

8 The proposed solution approach derives the system toward the prescribed objective based on the current network conditions. LaSalle's theorem, an extension of the classical Lyapunev approach is used to perform the stability analysis. The analysis addresses the global behavior of the route guidance control strategies. Smith (1979, 1984) first addressed the stability of traffic network equilibrium for the static traffic assignment problem. Horowitz (1984) proposed three models for the route choice decision-making process in a two-link network based on three weighted average measures. Zhang and Nagurney (1995, 1996), Nagurney and Zhang (1996, 1997) introduced the projected dynamical system concept to study the route choice adjustment process in both elastic and fixed demand networks. They proposed two distinct approaches: the monotonicity approach to analyze global stability and the regularity approach for local stability analysis. Watling (1999) extended Horowitz's results (1984) to general networks. A route switching control strategy based on Smith (1984) is used to assign time-dependent traffic demand to the network. In this analysis, they find that travel costs play an equivalent role in traffic assignment problems as energy does in mechanical systems. This affords a general stability analysis procedure for traffic assignment problems.

Han (2003) of Centre for Transport Studies, UCL, Gower Street, London, UK presented a paper on "Dynamic traffic modeling and dynamic stochastic user equilibrium assignment for general road networks". In this paper, he investigated the requirements of dynamic traffic modeling and proposed the deterministic queuing model as a plausible link performance function to describe the relation ship between inflows, outflows, and link travel costs in time varying condition. Then, it explained how he can perform logit-based stochastic network loading for general road networks in the dynamic case. In particular, he showed in this paper how to perform dynamic stochastic network loadings for many to many origin- destination pairs and what should be considered to maintain correct flow propagation in the network loading process. Then, it explains how the stochastic dynamic user equilibrium (SDUE) assignment problem can be solved without direct evaluation of the objective function. For this purpose, a quadratic

9 interpolation, the method of successive average, and the pure network loading method are adopted at the line-search step in the solution algorithm.

• Ridwan (2004) of RWTH Aachen University of technology, Aachen, Germany developed a model on "Fuzzy preference based traffic assignment". In this paper, it was discussed that travelers do not or cannot always follow the maximization principle. Therefore they formulate a model that takes in to account the travelers with non-maximizing behavior. The model is based on fuzzy preference relations. FiPV (fuzzy traveler preference) is a choice function based on fuzzy preference relations. A fuzzy preference relation is a fuzzy extended form of traditional crisp (YES or NO) preference relations. They adopt some ideas of alternatives perception and mental map that can reduce hundreds of possible alternatives to a limited number of real potentially available path alternatives that are actually faced by travelers. They developed a concept of decision segment, which consists of decision nodes that may be expanded as necessary. Decision segment is a subset of eigen network that can be interpreted as individual,. awareness of the existing network. FiPV analysed the decision problem within this., decision segment. Teodorovic and Kikuchi (1990) were first to model the complex route choice problem using fuzzy logic. They used fuzzy inference techniques to, study the binary route choice problem. Akiyama et al. (1993) developed a modd, for route choice behavior based on the fuzzy reasoning approach. Lotan and Koutsopoulos (1993) developed models for route choice behavior in the presence of information based on concepts frdirf approximate reasoning and fuzzy control. In modeling Birmingham—Belgrade route choice, Radojevic and Petrovic (1997) proposed fuzzy sets theory and associate approximate reasoning as an appropriate framework to imitate human reasoning in expressing a preference structure. Henn (1997) suggested a fuzzy version of a deterministic choice model and proved that fuzzy route choice model is a generalization of the standard logit model, in which the modeling approach is seen as a general framework of random utility based models. Akiyama and Tsuboi (1998) used multi-stage fuzzy reasoning to describe the driver decision making process on road networks. Their paper considers the

10 multi-route choice problem. Zhao (1994) proposed a new concept of user equilibrium: the 6-equilibrium. Driver's perception of generalized travel time is modeled using a fuzzy number. Based on the perceived generalized travel times of the different route alternatives, drivers will choose a route which 'optimizes this fuzzy travel time. The paper proves that an s-equilibrium exists in which no user believes that changing his route choice on his own may very effectively reduce the generalized travel time. Herein, E conveys the indifference threshold of the drivers that is the change in the generalized travel time which the driver allows, before changing his route choice. Wang and Liao (1999) focused their study on solving a user equilibrium problem in traffic assignment when the node-arc incidence matrix is fuzzy. By considering it, as a variational inequality problem with fuzzy function in a convex cone, this problem is reformulated into a multiple objective programming model. Henn (1999) developed a route choice model based on possibility measure and defined a fuzzy user equilibrium (FUE), an extended UE for dynamic systems into near-equilibrium state. FUE means that "each used route has approximately the same cost and it is almost minimal". Chang and Chen (2000) used the variation inequality approach to formulate a link-based fuzzy user- optimal route choice problem embedding link interactions. Adler et al. (forthcoming) presented an approach for dynamic path evaluation based on fuzzy logic.

2.4 STUDIES CONDUCTED IN INDIA In India a model of capacity restraint route assignment technique was developed at I.I.T. Kharagpur. In this model the trips are allocates to a network to all possible paths from origin to destination and takes into account the capacity restraint in each link. This model is based on some assumptions: For each and every link impedance values are known and expressed in terms of travel time. Once a link attains its traffic capacity, no further trips are allotted to it. The probability of any trip, in excess of the capacity going in that link becomes zero. Distribution of trips from one node to every other node is proportional to the probability of usage of the corresponding links.

11 This model takes into consideration the probabilistic behavior of road users and the capacity restrictions of the links in a network. Here, it is not necessary to define efficient paths in the network to assign traffic. It allows incorporating the change in impedance values with change in traffic volumes.

A software on route assignment with name "SHORT-PATH" was developed by `Maurya A.K.' at University of Roorkee. The salient features of the software are: 1. The method is based on all-or-nothing assignment technique. 2. To determine the shortest path Moore's algorithm is used 3. The source code is written in C language. 4. The software is user-friendly and interactive. 5. The software gives pictorial view of output.

At I.I.T. Roorkee Software titled "TRASCARE-2002" was developed ;by `Bains, N.S.'. The software was developed for route assignment by capacity restraint method. The salient features of this software are: 1. The software is based on capacity restrained method. 2. The source code of the software is written in C language and run in MS- DOS mode. 3. It is user-friendly and interactive. 4. The software contains four modules namely general module, design module, help module and I.R.C.-dode module. 5. Graphics is added to the software to give attractive colors and produce pictorial view of the connected network. 6. The user can feed the data using a standard input data file. 7. The user has an option to modify the input data if he wishes, after the entry of all the data. 8. All the entered input data are displayed on the screen.

12 9. The output is given in the form of pictorial views of the output network at the end of each iteration. It is allowed to exit from the software at the end of each iteration or revise the number of iterations. To validate this software he conducted field survey in Jaipur city. The results obtained using the "TRASCARE-2002" software matched with the results obtained by manual calculation, proving the fruitfulness of the software.

At I.I.T. Roorkee software titled "RAMP 2003" was developed by `Chattaraj, Ujjal'. The software was developed for route assignment by multipath route assignment technique method. The salient features of this software are: 1. The software is based on multipath route assignment technique. 2. The source code of the software is written in C language and run in MS- DOS mode. 3. It is user-friendly and interactive. 4. The user has an option to modify the input data if he wishes, after the entry of all the data. 5. All the entered input data are displayed on the screen. 6. The output is given in the form of pictorial views of the output network at the end of each iteration. It is allowed to exit from the software at the end of each iteration or revise the number of iterations.

13- CHAPTER-3 TRANSPORTATION PLANNING 3.1 GENERAL The most important aspect of planning is the fact that it is oriented . towards the future. A planning activity occurs during one time period but it is concerned with actions to be taken at various times in the future. The fundamental purpose of transportation planning is to provide efficient access to various activities that satisfy human needs. Therefore, the general goal of transportation planning is to accommodate this need for mobility. In this process, planners develop information about the impacts of implementing alternative courses of action involving transportation services, such as new highways, bus route changes, parking restrictions. This information is used to help decision makers in the selection of transportation policies and programs. The transportation planning process relies on travel demand forecasting, which involves predicting the impacts that various policies %nd programs will have on travel in the urban areas. The forecasting process also provides detailed information, such as traffic volumes, capacity to be used by traffic engineers and planners in their designs. Generally it is believed that the Urban Transportation Planning Process (UTPP) originated with the Chicago Area Transportation Study (CATS, 1959), in which traffic demands were forecasted based on the assumption that they were related to human travel behavior, land- use, and travel patterns. The UTPP has been the most popular tool for travel demand forecast in urban areas (Dickey, 1983). Papacostas (1993) defines UTPP as "to perform a conditional prediction of travel demand in order to estimate the likely transportation consequences of several transportation alternatives (including the do-nothing alternatives) that are being considered for implementation". This process is an iterative, sequential procedure for evaluation and selection of transportation projects to serve present and future land uses. It is also recognized as a long-term planning process to forecast the future demand by mode and evaluate alternative networks based on certain

14 scenarios. Throughout the years this sequential process has been refined with various techniques and methodologies.

3.2 TRAVEL DEMAND FORECAST Travel-demand Forecasting is an important phase of transportation planning. Initially, the projection of the inter-zonal trip distribution toward the target year was accomplished by applying simple growth factors to the base- year travel desire volume in a manner that was similar to rural highway practice. Gradually, however, it became evident that the need for added capacity and parking facilities in the urban area was not uniform throughout the region but was dependent on the specific types (e.g. residential, commercial or industrial) and intensities (residential density, workers per acre, shopping floor space and the like) of land used found in each zone. Moreover, the expected regional growth of the population and the economic system was unevenly distributed among the zones owing to differences in the availability and suitability of developable land for various purpbses, urban planning policies (such as zoning) and accessibility. Since the emphasis of these studies was placed on the urban highway system, transit trips had to be subtracted from the projected total inter-zonal traffic volumes to arrive at an estimate of future highway demands. The route choice models were later extended to cover large networks and became known as traffic assignment models. Thus trip-generation, trip-distribution, model choice and traffic-assignment models evolved, each intended to describe and forecast a different component of travel behavior.

3.3 SEQUENTIAL DEMAND FORECASTING MODELS The sequential demand forecasting models explained the purpose of the travel forecasting phase of the urban transportation-planning process. This prediction is also conditional on a predicted target-year land-use pattern. The major components of travel behavior were identified as 1. The decision to travel for a given purpose (trip generation). 2. The choice of destination (trip distribution).

15 3. The choice of travel mode (model choice). 4. The choice of route or path (network assignment).

Land use and soc ioeconornic projection

Trip generation

Transportation system specification

Trip distribution

Modal choice

Network assignment

Direct (user) impacts

Figure 3.1 The sequential demand forecasting process

Figure 3.1 illustrates that travel-demand models can be chained together in a sequence. In this sequential-demand-modeling arrangement, the outputs of each step become inputs to the following step. The most frequently used models for each of the four steps of the sequential process are covered in this chapter. For each model, the relevant dependent and independent variables are identified, and the method of calibration is described.

16 3.3.1 Trip Generation General The objective of a trip-generation model is to forecast the number of person- trips that will begin from or end in each travel analysis zone within the region for a typical day of the target year. Prior to its application, a trip generation model must be calibrated using observation taken during the base year by means of a variety of travel surveys. The total number of person-trips generated constitutes the dependent variable of the model. The independent or explanatory variables include land use and socio-economic factors that have been shown bear a relationship with trip making. When applying a calibrated trip-generation model predictive purpose, the numerical values of the independent variables must be supplied by the analyst. These values are obtained from the area wide land use and socio-economic projection phase, which precedes the trip-generation step. Trip purposes In contemporary transportation planning, the zonal trip making is estimated separately for each of a number of trip purposes, typically including work trips, school trips, shopping trips and social or recreational trips. The reason separate trip-generation models are usually developed for each trip purpose is that the travel behavior of trip makers depends on the trip purpose. For example, work trips are undertaken with daily regularity, mostly during the morning and after noon period of peak traffic and overwhelmingly from the same origins to the same destinations. There are following methods used for trip generation: Regression models If trip generation patterns and some socio-economic activity show considerable correlation, ordinary least-squares regression is often used to estimate the relationship between the number of trip productions and/or attractions. The general form of the multiple regressions is shown in following Equation:

Y = a0 + a1 X1 + a2 X2 + ar X,. Where Y is the dependent variable (i.e., the number of trips produced or attracted), the X's are the relevant independent or explanatory variables, and a's are

17 the parameters of the model. While trip production is expressed as function of socioeconomic data and/or population, trip attraction is expressed as function of land use, employment, and/or other economic activities (Hobeika, 1996). Regression models are relatively straight forward to implement, thus cost effective and the data needs are moderate in size (Meyer et al, 1984). Trips Produced = f (Socio-economic var., Population) Trips Attracted =f (Land use, Employment & other Economic Activities) Zonal versus Household based models A transportation planning can not possibly trace the travel patterns of every individual residing within a region. As a result, the geographical patterns of trip making are summarized by dividing the region in to smaller travel-analysis zones and by associating the estimated trips with these zones. These models were calibrated on a zonal basis, meaning that the overall zonal characteristics were used as independent or explanatory variables. These zonal attributes include variables such as the zonal population, the average zonal income, the average vehicle ownership and etc. For example, two zones may have the same average income (in the middle income range, for example) but one may be composed of a homogeneous group of households with respect to income. If income is not linearly related to trip generation, a zone-based (or aggregate) model will not be sensitive to: the intra-zonal income differences. Household based (or disaggregated) models of trip generation are also available. Production and Attraction The trips that are predicted by' a trip-generation model for each zone are often referred to as the trip ends associated with that zone. Trip ends may be classified either as origins and destinations, or as production and attractions. As used in trip-generation studies, the terms origin and production on one hand and destination and attraction on the other are not identical. The term origin and destinations are defined in terms of the direction of a given inter-zonal trip. On the other hand, the terms production attraction are not defined in terms of the directions of trips but in terms of the land use associated with each trip end.

18 A typical trip-generation study involves the application of residential trip- production and non-residential trip-attraction models. Trips can also be classified as home-based or as non-home-based.

3.3.2 Trip Distribution The next step in the sequential forecasting model system is concerned with the estimation of the target-year trip volumes that interchange between all pairs of trip-producing zone and trip-attracting zone. The number of trips generated in every zone of the study area has to be apportioned to the various zones to which these trips are attracted. The trip distribution matrix synthesized must satisfy the production and attraction trip-end constraint equations. Everything else being equal, more trips will be attracted by zones that have higher levels of "attractiveness". For example, the case of two identical shopping centers (i.e. of equal attractiveness) competing for the shopping trips produced by a given origin zone. If the distance between origin zone and each of the two centers are different, shoppers residing in origin zone will show a preference for the closer of two identical centers. Thus, the intervening difficulty of travel between the producing zone and each of the competing zones has a definite effect on the choice of attracting zone. The trip-distribution model estimates the inter-zonal person- -trip volumes based on the productions of each origin zone, the attractiveness of destination zone, and the inter-zonal impedance Wij. The most common mathematical formulations of trip distribution include various growth factor models, the gravity model, and a number of opportunities models. The fig 3.2 shows the estimation of trip distribution among estimated target year.

19 Trip end estimates from trip generation Di DJ

-pp Calibrated Trip Estimated Target Year Distribution model Tij

Target year estimates of inter-zonal impedanc e tj

Fig 3.2 Estimation of Trip Distribution

3.3.3 Modal Choice A modal choice or modal split model is concerned with the trip maker's behavior regarding the selection of travel mode. The mode choice is used to estimate future travel volumes by mode. This step is based on the concept that the mode- choice behavior of trip makers can be explained generally by three categories of factors, the characteristics of available modes; the socioeconomic status of the trip maker and the characteristics of the trip (Papacostas, 1993). The factors which determine the choice of a particular mode of travel depends on the factors, cost, distance, time, comfort, income of person. Usually mode choice models are classified into two groups according to the type of mathematical abstraction used; 1) aggregate models, and 2) disaggregate behavioral models. Statistical data are mainly considered in aggregate models, and for the latter the individual utility measures are considered. The aggregate models are differentiated according to the sequential procedure in which each model is applied. "Trip-end mode choice model", is processed just after the trip generation step. "Trip interchange mode choice model" is executed after the trip distribution model. In disaggregate behavioral models the term `disaggregate' means that the models are based on individual observations and the term 'behavioral' means that they reflect the actual choice process level on which the choice is made.

20

TripGtneration Trip Creneratiou

ip Ends Person-111 ip Ends

I Medal Split Trip diitibution

Trip olements TiM15ir dip ends Nontrausit trip Enth

Nfolial choice Transit trip Nutransit tip &suitIntim ditAibution

Traust trips Nontrar sit trips

Fig 3.3 Modal Choice Model

3.3.4 Trip Assignment The final stage of travel demand forecasting process is the trip assignment analysis. Trip assignment is the procedure by which route interchanges are allocated to different parts of the network forming the transportation system. During the analysis, the route to be traveled is determined and the inter-zonal flows are assigned to the selected routes. Trip assignment is concerned with the trip- maker's choice of route from one place to another on the transportation network. It is used to estimate the volume of traffic or passenger trips on various links of the transport network for any future year, or to simulate present conditions. The trip assignment requires as input a description of either existing or proposed transportation system or a trip table (a matrix of inter-zonal trip moments). The output will be an estimate of the traffic volumes on each link of the network system. Trip assignment procedure is based on the selection of a minimum time path over an actual route between zones. The basic assumption is that the traveler will use the 'best' route open to him. The best route may be fastest, or the cheapest or a combination' of both. The important point is that the route used for a journey

21 from one part of the city to another will be the one with the shortest travel time or the least travel cost. The following figure shows four stage urban transportation planning process (UTPP):

;-„-Tit. 4. 71PP $ , e ,.. kept -+3 me oeess: Same of _Esti Mo els. in Each Steps , - - '

0i- Di

Trip Generation • Repestion —IP' 4— • Cre...;-Classi5eation • Ttip-rate Attalysis

Trip till' tic., 4 . GrolvdtFactor Model • Czavityllodel • lutetveuittr C apcst.:t Model

'4.3 Mode Choice Drreiliois Curve lt,lotiei • DiraLgepte behavioral Model

. imifii Traffic Ihliel"t. • ..11.11-or-Notkinz Assigament AssirallliM 1111•11/ • C1P3City l'FAIZillt Av:ipursent m iiecarl

Fig 3.4 Four stage transportation planning process

22 CHAPTER-4 TRAFFIC ASSIGNMENT 4.1 GENERAL Traffic assignment is the process of allocating a set of present or future trip interchanges, known as origin-destination demands, to a specified transportation network. It is the last phase of the sequential transportation forecasting process and concerned with the trip-maker's choice of path between pair of zones by travel mode and with the resulting vehicular flows on the multimodal transportation network. The trip assignment requires as input a description of either existing or proposed transportation system or a trip table (a matrix of inter-zonal trip moments). The output will be an estimate of the traffic volumes on each link of the network system. Many highway planning and design decisions are based on the results of traffic-assignment forecasts. All urban areas use traffic forecast for following purposes: 1. To asses the deficiencies in the transportation network. 2. To evaluate the effects of limited improvements and expressions to the existing transportation system. 3. To develop construction priorities. 4. To test alternative transportation network proposals. 5. To obtain design-year traffic volumes for design of facilities. Trip assignment procedure is based on the selection of a minimum time path over an actual route between zones. The basic assumption is that the traveler will use the 'best' route open to him. The best route may be fastest, or the cheapest or a combination of both. The important point is that the route used for a journey from one part of the city to another will be the one with the shortest travel time or the least travel cost.

4.2 GENERAL PRINCIPLE All assignment techniques are based on route selection. The choice of the route is made on the basis of a number of criteria such as journey time,

23 distance, travel cost, comfort and convenience, safety, and level of service. The route selection is made manually for small jobs but large jobs make use of an electronic computer for this purpose. The information obtained from road inventories and speed and delay studies are used to describe the road network. The road network is described by a system of links and nodes. A link is a section of a road network between two intersections. A node is either the centroid of a zone or the intersection of two or more links. The network specifications are coded in a specified form for further analysis by computer. The computer then chooses the shortest path between zones assigns estimated trips to this path and accumulates traffic volumes or passenger trips for each section of the route. A procedure commonly adopted in traffic assignment studies is that which is known as "Moore's Algorithm". Moore developed a method for dealing with telephone calls on the basis of shortest path, and this method has been used in many computer programmes designed to assign the traffic in a street network.

4.3 ROUTE ASSIGNMENT TECHNIQUES Route assignment techniques determine the paths through which trips are assigned between zones. There are so many route assignment techniques. Among them the following four are the commonly adopted techniques: 1. All-or-nothing assignment 2. Capacity restraint assignment 3. Multiple Route assignment 4. Diversion curves 4.3.1 All-or-Nothing Assignment This is the simplest technique and is based on the premise that the route followed by traffic is one having the least travel resistance. The resistance itself can be measured in terms of travel time, distance, cost or a suitable combination of these parameters. This technique assumes that either all drivers prefer a particular route or no body will take that route. This method is based on Moore's algorithm.

24 Moore's algorithm The steps of the algorithm are as follows: Step 1: Initially a label is assigned to each node in the network. Node j label = [i, d (j)] Where i = node nearest to node j which is on the minimum travel path from the origin. d ( j ) = minimum travel distance from node j back to the origin centroid. Step 2: Initially each node is assigned a d (j) value of very large magnitude say, 99999. For origin node d (j), value is set to zero. As the tree is built up from the origin, the following sum is formed for each node. Node j sum= [d (i) + 1 (i, j)] Where d ( i) = travel time from the origin to node i, which has just been connected to the origin. I (i, j) = travel time along the link which connects node j to node i. Procedure 1. If the sum just obtained is greater than d (j) already determined for nodej then the node is bypassed. 2. If the sum is less than existing d (j), then it is replaced by new sum and i is changed in the label to *reflect the new connected link for node j back to the origin. 3. These sums are tested against d (j) values recorded for the nodes. 4. This process is continued until all nodes have been reached. The inputs required to find out the shortest path in the network are as follows: • Maximum number of nodes in the network. • Maximum number of links in the network. ' • Distance or travel time of each link in the network.

25 This technique gives the shortest path for each node from the origin of the network. It also calculates the total distance or travel time of each node from the origin. After finding the minimum paths, the trips between zones are loaded into the links making up the minimum path. Since, in this technique all trips between a given 0- D pair are loaded on the links comprising the minimum path and nothing is loaded on the other links; it is called as all-or-nothing assignment. -4.3.2 Capacity Restraint Technique This is the process in which the travel resistance of a link is increased according to a relation between the practical capacity of the link and the volume assigned to the link. This technique has been developed to overcome the inherent weakness of all or nothing assignment technique which takes no account of the capacity of the system between a pair of zones. This method assumed that if the traffic on a road is increased its resistance to flow is also increased. Some of the methods of capacity restraint method are given below: 1. Smock Method In this method, first the all-or-nothing assignment is worked out. In an iterative procedure, the link travel times are modified according to the function:

(-1) TA =Toe

TA .5To

Where To = original travel time

TA = adjusted travel time e = exponential base V = assigned volume C = computed link capacity

In the second iteration, the adjusted travel times TA are used to determine the minimum paths or trees.

26 2. The Bureau of Public Roads (B.P.R.) Method In this method, the formula used to update the link travel time is:

TN =T0 [1+ 0.15(-1114

Where TN = link travel time at assigned volume To = base travel time at zero volume (equals 0.87 travel time at practical capacity) V = volume C = capacity 3. Wayne Method The step which is taken in this method is as follows: (i) Minimum path trees are constructed for all origin zones based on travel times computed average speed under typical urban condition. (ii) Inter-zonal volumes are assigned to the minimum path tree on all or nothing basis. (iii) Link travel times are recalculated using the following expressions

-1 TN = Toe ( )

Where TN = travel time on a link for nth iteration.

To =original travel time on the link V = assigned volume C = capacity of the link (iv) New minimum path trees are constructed using the new travel times calculated in the previous step. (v) Inter-zonal trip interchanges are then assigned on an all or nothing basis to the new minimum path trees.

27 (vi) Return to step 3 until equilibrium occurs or until some predetermined cutoff part is reached. 4.3.3 Multipath Route assignment Technique All road users may not be able to judge the minimum path for themselves. It may also happen that all road users may not have the same criteria for judging the shortest route. These limitations of the all-or-nothing approach are recognized in the multiple route assignment technique. The method consists of assigning the inter zonal flow to a series of routes, the proportion of total flow assigned to each being a function of the length of that route in relation to the shortest route. In an approach suggested by "Burrell", it is assumed that a driver does not know the actual travel times, but that he associates with each link a supposed time. This supposed time is drawn at random from a distribution of times, having as its mean the actual link time. The driver is then assumed to select the route which minimizes the sum of his supposed link times. Multiple route models have been found to yield more accurate assignment than all-or-nothing assignments. This technique recognizes that several paths between two nodes might have nearly equal impedance, and therefore, equal use. So, there is some probability that even longer route will be taken by some travelers. In this technique, trips are assigned to reasonable paths between zones as a function of the relative impedance of the path. Thus, paths of equal impedance receive equal traffic and longer paths, less traffic. In this technique, a path between zones is considered only if every link in it have initial node closer to the origin than the final node. The steps proposed at I.I.T. Kharagpur to this technique are as follows: (1) In order to assign trips between a particular node and a destination node through a node network, the shortest path is determined using reverse of Moore's algorithm, which is designated as SP[i]. Where `i' is that particular node. (2) Distance from node i to j is calculated on the basis of following formula: Distance (i, j) = SP (j) + Impedance (i, j)

28 Where Impedance (i, j) = Link length from node i to j. SP (j) = Shortest path for node j. (3) The probability of trips going from each node to all the emanating links are calculated using the following formula: 1 dis tan ce(i, j) E = 1 dis tan ce(i, m)

Where, Pr (i, j) = Probability of trip from node i to node j. E = A constant of model. m = Number of links meeting at node i. (4) In the first stage for each O-D pairs, trips are assigned from the origin node to the connected links using the probability matrix constructed in step 2. Accumulated trips in each node are determined and assigned to the connected links in the second stage using the probability matrix. In this way, stage by stage more and more number of new nodes is reached. Since, backtracking is allowed; some trips may accumulate at the nodes for which assignment has already been done. (5) Procedure described in step 4 is repeated until all the trips from the origin node has been reached at the destination node (this also ensures that there are no accumulated trips at any of the nodes) of each 0-D pairs. In this way trips are distributed among the links irrespectiVe of the capacity restrictions of the links. Some common multi-path assignment techniques are given below: (1) Mc Laughlin multi-path technique This is the first multi-path assignment technique, which uses the driver's route selection criteria. These criteria depend on travel time, travel cost and accident potential. The impedances in each link are determined at the zero traffic volume. With the help of these, the minimum resistance paths between each O-D

29 pair are calculated. This minimum resistance value is increased by 30%, which is called the maximum resistance value. All the paths between O-D pair with resistance values less than this maximum value are identified. Mc Laughlin uses the principle of linear graph theory for his multi-path assignment technique. This technique has been applied in Ontario, Canada. (ii) Dial's multi-path assignment technique In this technique, all reasonable paths between a given origin and destination are given a non-zero probability of use. When a traveler by traversing each link goes further away from origin and comes closer to destination, the path is considered as reasonable. This technique probabilistically assigns trips to paths instead of explicitly assigning them. The fraction of trips assigned to each alternate link is a probability based on the comparative length and number of efficient paths through the link. When backtracking comes into picture, a path is considered unreasonable. But in reality, a traveler may backtrack if by doing so, he finds that the distance required to reach the destination is not significantly high as compared to the alternative reasonable paths and other factors are favorable. iii) Burrell's multi-path assignment technique In this technique it is assumed that user does not know the actual travel times on links but associates a supposed travel time on each link that is drawn at random from a distribution of times. It is assumed that the user finds and uses a route, which minimizes the sum of the supposed link times. This technique has been applied in Karlsruhe, Germany. 1.3.4 Capacity Restraint Multipath Route Assignment Technique This method is almost same as multipath route assignment technique but in this technique we have also consider the capacity of each link instead of only distance. This method can be considered as combination of capacity restraint and multipath technique. The steps followed in this technique are as follows: (1) In order to assign trips between a particular node and a destination node through a node network , the shortest path is determined using reverse of Moore's algorithm, which is designated as SP[i].where T is that particular node.

30 (2) Distance from node i to j is calculated on the basis of following formula: DISTANCE (i, j) = SP (j) + IMPEDEINCE (i, j) Where IMPEDANCE (i, j) = Link length from node i to j. SP (j) = Shortest path for node j. (3) The probability of trips going from each node to all the emanating links are calculated using the following formula: 1 dis tan ce(i, j)E PO, 1 dis tan ce(i,m)E

Where, Pr (i, j) = Probability of trip from node i to node j. E = A constant of model. m = Number of links meeting at node i. (4) In the first stage for each O-D pairs, trips are assigned from the origin node to the connected links using the probability matrix constructed in step 2. Accumulated trips in each node are determined and assigned to the connected links in the second stage using the probability matrix. In this way, stage by stage more and more number of new nodes is reached. Since, backtracking is allowed; some trips may accumulate at the nodes for which assignment has already been done. (5) Procedure described in step 3 is repeated until all the trips from the origin node has been reached at the destination node (this also ensures that there are no accumulated trips at any of the nodes) of each O-D pairs. In this way trips are distributed among the links irrespective of the capacity restrictions of the links. (6) For each link the ratio of trips assigned due to all the O-D pairs to the capacity are calculated. If the ratio in all the links are less than or equal to 1, the assignment is complete.

31 (7) If the ratio is greater than 1 in one or more number of links, the highest value of the total assigned volume to capacity ratio (Rm) is determined and the corresponding link is identified. The number of originating trips and assigned trips calculated in each link (due to each individual O-D pair and all the O-D pairs) is reduced by dividing corresponding volumes by Rm. The assignment for the reduced volume is now complete (set 1). (8) For assigning the remaining trips, the link with the highest assigned volume to capacity ratio (i.e. greater than 1) in previous step is not considered as it has already reached its capacity. With the remaining trips steps 1 to 6 are repeated (set 2). (9) Step 7 is repeated until the ratios of assigned total volume to capacity in all the links become less than or equal to 1. Thus a number of set of assignment are obtained, (set 3, 4, , n). (10) Corresponding link volumes (both for individual O-D pairs and all the O-D pairs) obtained from different sets are now added to get the final assigned volume. (11) If finally for all the links total volume becomes equal to the capacity and still traffic remains in origin of any O-D pair it means that the existing road network of that urban area is unsuitable for smooth operation with that amount of traffic measures should be taken to increase the capacity of the roads. 4.3.4 Diversion Curves Diversion curves represent empirically derived relationship showing the proportion of traffic that is likely to be diverted on a new facility (bypass, new expressway, new arterial street etc.) once such a facility is constructed. The curve is constructed by the data collected from the pattern of road usage in the past. Diversion curves can be constructed using variety of variable such as: • Travel time saved. • Distance saved. • Travel time ratio. • Distance ratio. • Travel time and distance saved. • Distance and speed ratio. • Travel cost ratio

32 Bureau of public road diversion curve gives the following formula which has been fitted to this type of curves:

100 P 1+

Where P = percentage traffic diverted to new system tR = travel time ratio

tR = time on new system / time on old system

100

90 ERCENT) P 80 Y ( 70 RWA

OTO 60

F M $0

40 EAGE O S

U 30

ZONE 20

TO- 10

ZONE- 0 04 0.6 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 i 4

TRAVEL TIME RATIO

Figure 4.1 Bureau of Public Road Diversion Curve The California diversion curve gives the following formula, which has been fitted to this type of curves. 50(d + 0.5t) p= 50+ 105 1.(d — 0.502 +4.5]

Where P = percentage of motorway usage d = distance saved in miles t time saved in minutes

33 N1111111111111111111111111101110111111111111111 INMINNINIZNEN111111111111111111111111111 1111111IMMINMEN111111111

IlkiiiMMIELMICIUTIMI 11 1111111111INIUMMINIMMIN 11111111111111M11161 1111111111MIN ■ 11111111111.110111=111111111M11111111 1111111111111011111111111111111111111111111011111 —4 —2 0 #2 +4 +6 +6 *10 +12 TIME SAVE D USING MOTORWAY IN MINUTES

Figure 4.2 California Diversion Curve

4.4 ELEMENTS OF TRAFFIC ASSIGNMENT The element of computerized traffic assignment models consist of five basic elements: I. preparing the network, 2. establishing the origin-destination demands, 3. identifying a traffic-assignment technique, 4. calibrating and validating a model, and 5. forecasting

4.4.1 Preparing Network All traffic-assignment computer models require representation of the network in terms of link and nodes. The method of representing various components of the network includes the following: • Intersection • Interchanges and weaving sections • Centroids and Connectors

34 4.4.2 Establishing Origin-Destination Demands The evaluation of future improvement is established by origin-destination demand matrix for the horizon year. The O-D matrix for the base year is first established by using conventional surveys like road side interview, postcard surveys, and home or phone interview among others. For short-range analysis, the base year O-D matrix can be adjusted to represent the horizon year by using any of the growth factor methods (Hutchinson 1974). For long-range analysis, the base year O-D matrix is used along with the land-use, economic, population, and transportation network data to estimate the future O-D matrix. These activities constitute the first three steps of the four—step transportation planning process (trip generation, trip distribution, modal split). 4.4.3 Identifying Traffic-Assignment Technique All computerized traffic-assignment techniques are based on an underlying assumption of user equilibrium, which postulates that trip makers choose their routes to minimize their own individual travel times or costs (Wardrop 1952). Wardrop also discusses another approach, referred to as system equilibrium, in which traffic is assigned to a network in such a way as to minimize the system wide average travel time. This approach is not particularly suited to normal road networks, but it is reasonable for networks with a single decision-making entity that would distribute trips among routes to achieve system equilibrium (Manheim 1979). User equilibrium is achieved using mathematical optimization, which not only guarantees convergence for convex link-performance functions, but is also capable of accommodating large-scale networks (Beckman et al. 1956; LeBlanc et al.1975). This technique has been extended to capacitated networks by Daganzo (1977a) and is readily available in computer packages, such as UTPS ("Computer" 1977) and EMME/2 (Florian et al.1979; Babin et al.1982). The drawback of this technique is that it may be difficult to understand with only limited documentation of its application.

35 4.4.3 Calibration and Validation Calibration Calibration of a traffic assignment model consists of two tasks: 1. Parameter estimation 2. Model calibration Parameter estimation consists of estimating certain parameters based on observed data for the base year. These parameters include: • Parameters of the demand functions for trip generation, trip distribution, model split (when they are combined with traffic assignment); • Parameters of variable demand functions; • Parameters of the multinomial logit and multinomial probit that are used in stochastic traffic assignment; and • Parameters of the link-performance function, which is used in all traffic-assignment techniques, except all-or-nothing. There are various method for estimating these parameters, including the least-squares and maximum-likelihood techniques (Sheffi 1985). The parameters of the link-performance function can also be estimated using simplified graphical methods (Easa 1982; May 1990). The second task model calibration means adjusting some elements of the traffic-assignment model so that it can reproduce the vehicular travel taking place in the transportation system as accurately as possible. Validation Validation is the process of comparing observed measures of performance for the base year with those predicted by the model. Validation can be performed by overall comparison of predicted and observed link volumes and route travel times, by screen-line comparison of predicted and observed link volumes and by comparison of predicted and observed vehicle miles of travel by facility type (Florian and Nguyen 1976; Janson et al.1986; Pedersen and Samadahl 1982). If the predicted and observed results are reasonably close, then the model is considered

36 valid. Otherwise, the model needs to be calibrated to achieve closer correspondence. Forecasting The final stage of applying a traffic-assignment model is to use the validated model to evaluate the impacts of proposed improvements or changes to the study area; a toolbox for such improvements has been developed by Meyer et al. (1989). The O-D matrix and the network must correspond to the horizon year. The network and the O-D matrix of the horizon year are modified, depending on whether the. type of improvement is supply or demand related. The model is then run with modified data and the impacts predicted. In this stage, the sensitivity of the forecasts to key modeling assumptions should ideally be examined (Meyer and Miller 1984).

4.4 PRACTICAL PROBLEMS IN TRAFFIC ASSIGNMENT This section describes various problems of traffic assignment. The problems are classified in to four categories: 1. network representation problems; 2. system-sub area data-translation problems; 3. model-calibration problems; and 4. forecasting problems Network Representation Problem Network representation problem consists of micro-macro network coding, prohibiting through movements via centroids, coding of permissible U-turns, coding of operational strategies, level of details and network aggregation. System-Sub area data-translation problems System-sub area data translation problems consist of refinement of computerized traffic-volume forecasts, traffic data for more detailed networks. Model-Calibration problems Model calibration problems consist of base year O-D matrix, network representation, assignment technique, link performance function.

37 Forecasting problems Forecasting problems consists of updating old O-D matrix, traffic volumes for different forecast year, checking accuracy of traffic forecasts, site impact studies.

38 CHAPTER-5 SOFTWARE DEVELOPMENT 5.1 GENERAL Computers have become the most powerful and versatile design tools in this modem era of sophisticated technology. These high speed and large memory digital devices have made significant contribution in all fields of civil engineering for design optimization and obtaining the desired output in surprisingly quick time. Computer applications in the field of transportation planning have a vast scope in developing countries like India. Currently, many transportation planning computer software packages available in the global market. It already has certain of these features, although the actual capabilities of these packages for solving real world problems vary in their flexibility, data manipulation power, and underlying theory. The software is not designed keeping in mind the Indian road condition. So, the software is not most effective for Indian roads. So, it is necessary to develop software to keeping in mind of Indian road condition. But, no significant work has been done in India to develop software on route assignment in urban areas. Keeping this in mind it is intended to develop software on route assignment in urban areas. This is done on the basis of principle of multipath route assignment technique.

5.2 SOFTWARE REVIEW The software review process established a list of packages likely to be applicable, researched available literature, and tested some packages with sample problems. One major resource is the "Software and Source Book" published by the Center for Microcomputers in Transportation, a transportation technology transfer agency established by the U.S. Department of Transportation at the University of Florida. This reference contains introductory information on virtually all of the transportation planning and traffic operations analysis packages. The names and developers of the selected packages are listed in Table 5.1.

39 Table 5.1 Software Packages and Developer

NAME DEVELOPER MINUTP Comsis Corp TMODEL2 Professional Solutions. Inc. TRANPLAN The Urban Analysis Group CARS Roger Creighton Asso. Inc MicroTRIPS MVA Systematica, UK EMME University of Montreal FREQ University of California, Berkeley NETSIM KLD Asso. Inc.

All of this software, except FREQ and NETSIM, are comprehensive transportation planning packages designed to handle highway networks, manipulate trip matrices, and perform traffic assignment. These packages were developed to emphasize broad network investment and capacity-allocation issues, rather than the operating efficiency of specific facilities. FREQ and NETSIM, on the other hand, were developed specifically for highway and urban arterials operational analysis.

5.3 SOFTWARE PRINCIPLE Currently, equilibrium traffic assignment, based on Wardrop's Principle, is available in many of the computer packages. This trip assignment method, with suitable preprocessing of the network representation and demand matrices, should fulfill the trip assignment tasks required in the proposed model. However, the algorithms used to implement equilibrium assignment in the different computer packages are different, which implies that the outputs from these models may vary somewhat. These differences are unimportant as long as the algorithm is a correct implementation of the equilibrium principle. Within a traffic network, users choose their routes to minimize individual perceived travel cost. On the other hand, from a transportation planning perspective, it would be desirable to allocate

40 . the users within the network in such a way as to minimize the total travel cost within the system. The former is the user-optimum equilibrium trip assignment and the latter is the system-optimum equilibrium trip assignment. The user-optimum equilibrium within a traffic network is thought to represent people's travel behavior, assuming logical decision making and perfect knowledge of conditions. Assuming complete knowledge of their available options, users should always take the shortest path between a particular origin-destination (0-D) pair. But all users would not necessarily take the same path, due to capacity restraints on links between the O-D pair. They may be split among a few equally shortest paths within the network. The equilibrium is reached when the users assigned to different paths can no longer improve their individual travel costs by unilaterally switching to other paths. However, in general, the user-optimum equilibrium does not minimize the total travel cost in the system. The system-optimum trip assignment method allocates traffic among the paths within the network between different O-D's in such a way as to minimize the total travel cost in the system. Under this form of equilibrium, the marginal costs on all alternative paths utilized between each O-D pair are equal. However, the user's individual travel costs are generally not minimized. It should be realized, as Kanafani stated in "Transportation Demand Analysis", that the system-optimum equilibrium does not represent typical user'S behavior. Rather, it is a tool to analyze the situation when some means of traffic control is contemplated to move the pattern of trips from user optimum toward system optimal.

5.4 SOFTWARE DEVELOPMENT PROCEDURE The procedure which is used to develop software for Capacity restrained Multipath technique is as follows: (1) In order to assign trips between a particular node and a destination node through a node network , the shortest path is determined using reverse of Moore's algorithm, which is designated as SP[i].where `i' is that particular node. (2) Distance from node i to j is calculated on the basis of following formula:

41 Distance (i, j) = SP (j) + Impedance (i, j) Where Impedance (i, j) = Link length from node i to j. SP (j) = Shortest path for node j. (3) The probability of trips going from each node to all the emanating links are calculated using the following formula: 1

p(i , p = dis tan ce(i, j)E

dis tan ce(i, m)E

Where, Pr (i; j) = Probability of trip from node i to node j. E = A constant of model. m = Number of links meeting at node i. (4) In the first stage for each O-D pairs, trips are assigned from the origin node to the connected links using the probability matrix constructed in step 3. Accumulated trips in each node are determined and assigned to the connected links, in the second stage using the probability matrix. In this way, stage by stage more and more number of new nodes is reached. Since, backtracking is allowed; some trips may accumulate at the nodes for which assignment has already been done. (5) Procedure described in step 3 is repeated until all the trips from the origin node has been reached at the destination node (this also ensures that there are no accumulated trips at any of the nodes) of each O-D pairs. In this way trips are distributed among the links irrespective of the capacity restrictions of the links. (6) For each link the ratio of trips assigned due to all the O-D pairs to the capacity are calculated. If the ratio in all the links are less than or equal to 1, the assignment is complete. (7) If the ratio is greater than 1 in one or more number of links, the highest value of the total assigned volume to capacity ratio (Rm) is determined and the

42 corresponding link is identified. The number of originating trips and assigned trips calculated in each link (due to each individual O-D pair and all the O-D pairs) is reduced by dividing corresponding volumes by R.. The assignment for the reduced volume is now complete (set 1). (8) For assigning the remaining trips, the link with the highest assigned volume to capacity ratio (i.e. greater than 1) in previous step is not considered as it has already reached its capacity. With the remaining trips steps 1 to 6 are repeated (set 2). (9) Step 7 is repeated until the ratios of assigned total volume to capacity in all the links become less than or equal to 1. Thus a number of set of assignment are obtained, (set 3, 4, ....., n). (10) Corresponding link volumes (both for individual O-D pairs and all the O-D pairs) obtained from different sets are now added to get the final assigned volume. (11) If finally for all the links total volume becomes equal to the capacity and still traffic remains in origin of any O-D pair it means that the existing road network of that urban area is unsuitable for smooth operation with that amount of traffic measures should betaken to increase the capacity of the roads.

43

5.5 FLOW CHART

C START

Enter No. of node No. of link Link distance Link capacity Traffic at origin

calculation of shortest path construction of distance matrix distance matrix=a[i][j] where Ffrom node Fto node

initialization of matrix m

m[i]U7 = infinity m[i][j] = 0

■--11110, m[i] D.1

A

44

V For k=1 to node For i=1 to node for 1 to node

sp[i] =m[i][11 sp[i]= m[i][11-1-m[k] Di

sp[]

Calculation of distance of each link distance[i][11=spOPrimpedance[][j]

calculation of probability matrix Prig Lil

45 Calculation of traffic volume at each link

Fori 1tonode for to node MilLB=Vill*Pr[g LI1

Calrulation of ratio of assigned volume to capacity

For i=1 to node for j1 to node LiliCti]

fil=v[i]

V

Terminate

46 C

Calculation of new shortest path

initialization of matrix m

m[i][1] = infinity m[7G] = 0

For k=-1 to node For 1=1 to node for P 1 to node

sp[i] =m[i][i] sP[i1=

sp[i]

47 Calculation of distance of each link distance[i][j]=sp[j]+impedance[i]rj]

calculation of probability matrix Pr[i]

Calculation of traffic volume at each link

For i=1 to node for j=1 to node V[i1W—V[1*Pr[i]

Terminate

48 5.6 MODULE OF SOFTWARE The software is divided in to four modules: a. General Module b. Input Module c. Output Module d. Help Module General Module This module introduce about the name of-the software and name of the software developer. In this module user enter the password for running the software. Screenprint of this module is shown below:

ARE ASSIGNMENT

DEVELOPED." . 1:114tts44EET KUMAR M.TEGH, `CAD

UNDER GUIDANCE OF DR. PRAVEEN KUMAR ASSOCIATE PROFESSOR _.„civiL-ENGG.DEPARTMENT ROORKEE

Fig. 5.1 Screen Print of General Module

49 Input Module In this module user enter the traffic data. This is divided in five parts, which is as follows: (i) Input Data 1 (ii) Input Data 2 (iii) Input Data 3 (iv) Input Data 4 (v) Input Data 5 Input Data 1 module: In this module user enter the number of node and the number of link, which connect that node.

1)P411160it

,$.°,iiik,MUU Pa

Fig. 5.2 Screen Print of Input Data 1 Module Input Data 2 modules: This module is used for finding out the pictorial view of output. So that user represents the network by giving co-ordinate to each node. The input of this module consists of: (i) Node no. (ii) X- coordinate (iii) Y- coordinate

MULTIPAIVIC)14TASSi.PNOrtq TECt191)E

Fig. 5.3 Screen Print of Input Data 2 Module

51 Input Data 3 module: In this module user enter the node distance or travel time for each link. Link is represented by from node to node. The input of this module is: (i) From Node (ii) To Node (iii) Travel time/Distance

mu:ARA:al purr Assie,tvErA TEcHNIQuE,

iftER 11NrANCi'DIStA4CE• fTRAVEL

(3 Norton'

Fig. 5.4 Screen Print of Input Data 3 Module

52 Input Data 4 module: In this module user enter the traffic volume and capacity of each link. Link is represented by from node to node. (i) From Node (ii) To Node (iii) Traffic Volume

(iv) Traffic Capacity

-CA fAuLTPROP.UIL WIRSIEVITKUNTI tie . InPut QutP9t bet.

Fig. 5.5 Screen Print of Input Data 4 Module

53 Input Data 5 Module: In this module user enter the no. of origin destination pair and traffic flow from origin to destination. The input data is: (i) From Node (ii) To Node (iii)Traffic Flow or trip distribution

!vii4u6VATI-1‘,1101.1111,14GtAiVig;17411191-t ° atit-put Ewp°

TRIP DISTRIBUTIOtl~

Fig. 5.6 Screen Print of Input Data 5 Module

54 Output Module Output module consists of results and pictorial view of output. Result consist of following output for multipath route assignment and capacity restrained multipath route assignment: (i) Shortest path distance (ii) Distance (iii) Probability matrix (iv) Traffic volume (v) Pictorial view

04Q12itAT.t'ROVT— 13 tetiMIN'T: israRlIQUE NMAP — -

MULTIPATH ROUTE ASSIGNMENT:,i

SHORTEST PATH iDISTANCE

DISTANCE

PROBABILITY MATRIX

TRAFFIC VOLUME

PICTORIAL VIEW

CAPACITY RESTRAINED MULTIPATH ROUTE ASSIGNMENT:

SHORTEST PATH DISTANCE

DISTANCE

PROBABILITY MATRIX ra

TRAFFIC VOLUME

PICTORIAL VIEW

EXIT

Fig. 5.6 Screen Print of Output Result Module

55 Help Module Help module help the user in using the software and introduces about the technique which is used for route assignment.

5.7 FEATURES OF SOFTWARE 1. The software has been developed in visual basic. 2. The software developed is highly interactive and user friendly. 3. The software gives the pictorial view of output. 4. The software gives the approximate result as calculated. 5. The software work for large network which is manually not possible. 6. The software can be used anywhere at any instant. 7. The software has a feature of work for new data and save the data and user can open save data any time and started work on save data. 8. The user can modify input data anytime and show the final result in text form and pictorial view of output. 9. The software contains the help file which introduces the user to method of route assignment and how to use the software. 10. The software is highly secured against the unauthorized access.

56 CHAPTER-6 VALIDATION OF THE SOFTWARE 6.1 GENERAL After developing software, it is necessary to validate the model by developed software, so that software may become reliable. For validating the model, Allahabad city road plan was used taken from map-plan of Allahabad city. The data which has to be taken is link length, and their link capacity according to IRC code 106-1990. For validating the software the data of the city is used as input and then output is calculated by software and manually. After that both results are compared.

6.2 DATA FOR VALIDATION The following figure and data shows the road network of the some major road of the Allahabad city which has been used to validating the software.

Fig 6.1 Initial Road Network and their Distance

57 Table 6.1 Road Network Data

S.NO. LINK LENGTH CAPACITY (In Km) (In PCU/hr) 1 1-2 2 3600 2 1-5 4.5 1500 3 2-3 1.5 3600 4 2-4 1.5 3600 5 3-5 1.6 1500 6 3-6 1.5 3600 7 4-7 1.8 3600 8 5-6 1.4 1500 9 6-7 1 1000

Traffic flow from node 1 to 7 = 2000 PCU/hr. 6.3 ANALYSIS OF DATA The data taken is analyzed by using manual calculation and by computer application using developed software. At the end, both the results are compared. 6.3.1 Manual Analysis Step 1: First to determine shortest path from each node to destination by using reverse of Moore's algorithm, it is designated as SP[i].where T is that particular node. SP [1] = 2 + 1.5 + 1.8 = 5.3 SP [2] = 1.5 + 1.8 = 3.3 SP [3] = 1.5 + 1 = 2.5 SP [4] = 1.8 SP [5] = 1.4 + 1 = 2.4 SP [6] = 1 SP [7] = 0

58 Fig 6.2 Shortest Path Distance for each Node to Destination

Step 2: In second step, the distance from node i to j is determined on the basis of following formula: Distance (i, j) = SP (j) + Impedance (i, j) Where Impedance (i, j) = Link length from node i to j. SP (j) = Shortest path for node j.

Distance (1, 2) = 3.3 + 2 = 5.3 Distance (1, 5) = 2.4 + 4.5 = 6.9 Distance (2, 1) = 5.3 + 2 = 7.3 Distance (2, 3) = 2.5 + 1.5 = 4 Distance (2, 4) = 1.8 + 1.5 = 3.3 Distance (3, 2) =3.3 + 1.5 = 4.8

59 Distance (3, 5) = 2.4 + 1.6 = 4 Distance (3, 6) = 1 + 1.5 = 2.5 Distance (4, 2) = 3.3 + 1.5 = 4.8 Distance (4, 7) + 1.8 = 1.8 Distance (5, 1) = 5.3 + 4.5 =9.8 Distance (5, 3) = 2.5 + 1.6 = 4.1 Distance (5, 6) = 1 + 1.4 = 2.4 Distance (6, 3) =2.5+1.5=4 Distance (6, 5) =2.4 + 1.4=3.8 Distance (6, 7) = 0 + 1 = 1

Step 3: In third step, the probabilities of trips going from each node to all the emanating links are calculated using the following formula: 1 dis tan ce(i, j)E PO, i? E dis tan ce(i, m) Where, Pr (i, j) = Probability of trip from node i to node j. E = A constant of model. m = Number of links meeting at node i. Assume E = 1 P (1, 2) = 0.57 P (1, 5) = 0.43 P (2, 1) = 0.20 P (2, 3) = 0.36 P (2, 4) = 0.44 P (3, 2) = 0.24 P (3, 5) = 0.29 P (3, 6) = 0.47 P (4, 2) = 0.27 P (4, 7) = 0.73 P (5, 1) = 0.13 P (5, 3) = 0.32 P(5,6) =0.55 P (6, 3) = 0.17 P (6, 5) = 0.17 P (6, 7) 7.0.66 Step 4: In fourth step, trips are assigned from the origin node to the connected links using the probability matrix constructed in step 3. Accumulated trips in each

60 node are determined and assigned to the connected links in the second stage using the probability matrix. In this way, stage by stage more and more numbers of new nodes are reached. Since, backtracking is allowed; some trips may accumulate at the nodes for which assignment has already been done. 1st iteration: V [1] [2] = 2000*0.57 = 1140 V [2] =1140 V [1] [5] = 2000*0.43 = 860 V [5] = 860 2nd iteration: V [2] [1] = 1140*0.20 = 228 V [1] = 228+111.8=339.8 V [2] [3] =1140*0.36 = 410.4 V [3] =410.4+275.2=685.6 V [2] [4] = 1140*0.44 = 501.6 V [4] = 501.6 V [5] [1] = 860*0.13 = 111.8 V [6] = 473 V [5] [3] = 860*0.32 = 275.2 V [5] [6] = 860*0.55=473 3rd iteration: V [1] [2] =339.8*0.57=193.7 V [2] =193.7+164.5+135.4=493.6 V [1] [5] =339.8*0.43=146.1 V [3] = 80.4 V [3] [2] =685.6*0.24=164.5 V [5] = 146.1+198.8+80.4=425.3 V [3] [5] =685,6*0.29-198.8 V [6] = 322.2 V [3] [6] =685.6*0.47=322.2 V [7] = 366.2+312.2=678.4 V [4] [2] =501.6*0.27=135.4 V•[4] [7] =501.6*0.73=366.2 V [6] [3] =473*0.17=80.4 V [6] [7] =473*0.66=312.2 4th iteration: V [2] [1] = 493.6*0.2=98.7 V [1] =98.7+55.3=154 V [2] [3] = 493.6*0.36=177.7 V [2] =19.3 V [2] [4] = 493.6*0.44=217.2 V [3] =177.7+136.1+54.8=368.6 V [3] [2] = 80.4*0.24=19.3 V [4] =217.2 V [3] [5] = 80.4*0.29=23.3 V [5] =23.3+54.8=78.1 V [3] [6] = 80.4 * 0.47 = 37.8 V [6] =37.8+233.9=271.7

61 V [5] [1] =425.3*0.13=55.3 V [7] =212.7+678.4=891.1 V [5] [3] = 425.3*0.32=136.1 V [5] [6] = 425.3*0.55 = 233.9 V [6] [3] = 322.2*0.17=54.8 V [6] [5] = 322.2*0.17=54.8 V [6] [7] = 322.2*0.66=212.7 5th iteration: V [1] [2] =154*0.57=87.8 V [1] =3.9+10.2=14.1 V [1] [5] = 154*0.43=66.2 V [2] =87.8+88.5+58.6=234.9 V [2] [1] = 19.3*0.2=3.9 V [3] =6.9+25+46.2=78.1 V [2] [3] =19.3*0.36=6.9 V [4] =8.5 V [2] [4] =19.3*0.44=8.5 V [5] =66.2+106.9+46.2=219.3 V [3] [2] =368.6*0.24=88.5 V [6] —173.2+42.9=216.1 V [3] [5] =368.6*0.29=106.9 V [7] =891.1+158.6+179.3=1229 V [3] [6] =368.6*0.47=173.2 V [4] [2] =217.2*0.27=58.6 V [4] [7] =217.2*0.73=158.6 V [5] [1] =78.19.13=10.2 V [5] [3] =78.1*0.32=25 V [5] [6] =78.1*0.55=42.9 V [6] [3] =271.7*0.17=46.2 V [6] [5] =271.7*0.17=46.2 V [6] [7] =271.7*0.66=179.3 6th iteration: V [1] [2] =14.1*0.57=8 V [1] =47+28.5=75.5 V [1] [5] = 14.1*0.43=6.1 V [2] =8+18.7+2.3=29 V [2] [1] = 234.9*0.2=47 V [3] =84.6+70.2+36.7=78.1 V [2] [3] =234.9*0.36=84.6 V [4] =103.4 V [2] [4] =234.9*0.44=103.4 V [5] =6.1+22.6+36.7=65.4 V [3] [2] =78.1*0.24=18.7 V [6] =36.7+120.6=157.3 V [3] [5] =78.1*0.29-22.6 V [7] =1229+6.2+142.6=1377.8

62 ✓ [3] [6] =78.1*0.47=36.7 ✓ [4] [2] =8.5*0.27=2.3 ✓ [4] [7] =8.5*0.73=6.2 ✓ [5] [1] =219.3*0.13=28.5 ✓ [5] [3] =219.3*0.32=70.2 ✓ [5] [6] =219.3*0.55=120.6 ✓ [6] [3] =216.1*0.17=36.7 ✓ [6] [5] =216.1*0.17=36.7 ✓ [6] [7] =216.1*0.66=142.6 7th iteration: V [1] [2] =75.5*0.57=43 V [1] =5.8+8.5=14.3 V [1] [5] = 75.5*0.43=32.5 V [2] =43+46+27.9=116.9 V [2] [1] = 29*0.2=5.8 V [3] =10.4+20.9+26.7=58 V [2] [3] =29*0.36=10.4 V [4] =12.8 V [2] [4] =29*0.44=12.8 V [5] =32.5+55.5+26.7=114.7 V [3] [2] =191.5*0.24=46 V [6] =90+36=126 V [3] [5] =191.5*0.29=55.5 V [7] =1377.8+75.5+103.8=1557.1 V [3] [6] =191.5*0.47=90 V [4] [2] =103.4*0.27=27.9 V [4] [7] =103.4*0.73=75.5 V [5] [1] =65.4*0.13=8.5 V [5] [3] =65.4*0.32=20.9 V [5] [6] =65.4*0.55=36 V [6] [3] =157.3*0.17=26.7 V [6] [5] =157.3*0.17=26.7 V [6] [7] =157.3*0.66=103.8 8th iteration: V [1] [2] =14.3*0.57=8.2 V [1] =23.4+14.9=38.3 V [1] [5] = 14.3*0.43=6.1 V [2] =8.2+13.9+3.5=25.6 V [2] [1] = 116.9*0.2=23.4 V [3] =42.1+36.7+21.4=100.2 V [2] [3] =116.9*0.36=42.1 V [4] =51.4

63 V [2] [4] =116.9*0.44=51.4 V [5] =6.1+16.8+21.4=44.3 V [3] [2] =58*0.24=13.9 V [6] =27.3+63.1=90.4 V [3] [5] =58*0.29=16.8 V [7] =1557.1+9.3+83.2=1649.6 V [3] [6] =58*0.47=27.3 V [4] [2] =12.8*0.27=3.5 V [4] [7] =12.8*0.73=9.3 V [5] [1] =114.7*0.13=14.9 V [5] [3] =114.7*0.32=36.7 V [5] [6] =114.7*0.55=63.1 V [6] [3] =126*0.17=21.4 V [6] [5] =126*0.17=21.4 V [6] [7] =126*0.66=83.2 9th iteration: V [1] [2] =38.3*0.57=21.8 V [1] =5.1+5.8=10.9 V [1] [5] = 38.3*0.43=16.5 V [2] =21.8+24+13.9=59.7 V [2] [1] = 25.6*0.2=5.1 V [3] =9.2+14.2+15.4=38.8 V [2] [3] =25.6*0.36=9.2 V [4] =11.3 V [2] [4] =25.6*0.44=11.3 V [5] =16.5+29+15.4=60.9 V [3] [2] =100.2*0.24=24 V [6] =47.1+24.4=71.5 V [3] [5] =100.2*0.29=29 V [7] =1649.6+37.5+59.7=1746.8 V [3] [6] =100.2*0.47=47.1 V [4] [2] =51.4*0.27=13.9 V [4] [7] =51.4*0.73=37.5 V [5] [1] =44.3*0.13=5.8 V [5] [3] =44.3*0.32=14.2 V [5] [6] =44.3*0.55=24.4 V [6] [3] =90.4*0.17=15.4 V [6] [5] =90.4*0.17=15.4 V [6] [7] =90.4*0.66=59.7 10th iteration:

V [1] [2] =10.9*0.57=6.2 V [1] =11.9+7.9=19.8

64 V [1] [5] = 10.9*0.43=4.7 V [2] =6.2+9.3+3.1=18.6 V [2] [1] = 59.7*0.2=11.9 V [3] =21.5+19.5+12.2=53.2 V [2] [3] =59.7*0.36=21.5 V [4] =26.3 V [2] [4] =59.7*0.44=26.3 V [5] =4.7+11.3+12.2=28.2 V [3] [2] =38.8*0.24=9.3 V [6] =18.2+33.5=51.7 V [3] [5] =38.8*0.29=11.3 V [7] =1746.8+8.2+47.2=1802.2 V [3] [6] =38.8*0.47=18.2 V [4] [2] =11.3*0.27=3.1 V [4] [7] =11.3*0.73=8.2 V [5] [1] =60.9*0.13=7.9 V [5] [3] =60.9*0.32=19.5 V [5] [6] =60.9*0.55=33.5 V [6] [3] =71.5*0.17=12.2 V [6] [5] =71.5*0.17=12.2 V [6] [7] =71.5*0.66=47.2 11t'' iteration: V [1] [2] =19.8*0.57=11.3 V [1] =3.7+3.7=7.4 V [1] [5] = 19.8*0.43=8.5 V [2] =11.3+12.8+7.1=31.2 V [2] [1] = 18.6*0.2=3.7 V [3] =6.7+9+8.8=24.5 V [2] [3] =18.6*0.36=6.7 V [4] =8.2 V [2] [4] =18.6*0.44=8.2 V [5] =8.5+15.4+8.8=32.7 V [3] [2] =53.2*0.24=12.8 V [6] =25+15.5=40.5 V [3] [5] =53.2*0.29=15.4 V [7] =1802.2+19.2+34.1=1855.5 . V [3] [6] =53.2*0.47=25 V [4] [2] =26.3*0.27=7.1 V [4] [7] =26.3*0.73=19.2 V [5] [1] =28.2*0.13=3.7 V [5] [3] =28.2*0.32=9 V [5] [6] =28.2*0.55=15.5 V [6] [3] =51.7*0.17=8.8 V [6] [5] =51.7*0.17=8.8

65 V [6] [7] =51.7*0.66=34.1 12th iteration: V [1] [2] =7.4*0.57=4.2 V [1] =6.2+4.3=10.5 V [1] [5] = 7.4*0.43=3.2 V [2] =4.2+5.9+2.2=12.3 V [2] [1] = 31.2*0.2=6.2 V [3] =11.2+10.5+6.9=28.6 V [2] [3] =31.2*0.36=11.2 V [4] =13.7 V [2] [4] =31.2*0.44=13.7 V [5] =3.2+7.1+6.9=17.2 V [3] [2] =24.5*0.24-5.9 V [6] =11.5+18=29.5 V [3] [5] =24.5*0.29=7.1 V [7] =1855.5+6+26.7=1888.2 V [3] [6] =24.5*0.47=11.5 V [4] [2] =8.2*0.27=2.2 V [4] [7] =8.2*0.73=6 V [5] [1] =32.7*0.13=4.3 V [5] [3] =32.7*0.32=10.5 V [5] [6] =32.7*0.55=18 V [6] [3] =40.5*0.17=6.9 V [6] [5] =40.5*0.17=6.9 V [6] [7] =40.5*0.66=26.7 13th iteration: V [1] [2] =10.5*0.57=6 V [1] =2.5+2.2=4.7 V [1] [5] = 10.5*0.43=4.5 V [2] =6+6.9+3.7=16.6 V [2] [1] = 12.3 *0.2=2.5 V [3] =4.4+5.5+5=14.9 V [2] [3] =12.3*0.36=4.4 V [4] =5.4 V [2] [4] =12.3*0.44=5.4 V [5] =4.5+8.3+5=17.8 V [3] [2] =28.6*0.24=6.9 V [6] =13.4+9.5=22.9 V [3] [5] =28.6*0.29=8.3 V [7] =1888.2+10+19.51917.7 V [3] [6] =28.6*0.47=13.4 V [4] [2] =13.7*0.27=3.7 V [4] [7] =13.7*0.73=10 V [5] [1] =17.2*0.13=2.2 V [5] [3] =17.2*0.32=5.5

66 V [5] [6] =17.2*0.55=9.5 V [6] [3] =29.5*0.17=5 V [6] [5] =29.5*0.17=5 V [6] [7] =29.5*0.66=19.5 14th iteration: V [1] [2] =4.7*0.57=2.7 V [1] =3.3+2.3=5.6 V [1] [5] = 4.7*0.43=2.0 V [2] =2.7+3.6+1.5=7.8 V [2] [1] = 16.6*0.2=3.3 V [3] =6+5.7+3.9=15.6 V [2] [3] =16.6*0.36=6 V [4] =7.3 V [2] [4] =16.6*0.44=7.3 V [5] —2+4.3+3.9=10.2 V [3] [2] =14.9*0.24=3.6 V [6] =7+9.8=16.8 V [3] [5] =14.9*0.29=4.3 V [7] =1917.7+3.9+15.1=1936.7 V [3] [6] =14.9*0.47=7 V [4] [2] =5.4*0.27=1.5 V [4] [7] =5.4*0.73=3.9 V [5] [1] =17.8*0.13=2.3 V [5] [3] =17.8*0.32=5.7 V [5] [6] =17.8*0.55=9.8 V [6] [3] =22.9*0.17=3.9 V [6] [5] =22.9*0.17=3.9 V [6] [7] =22.9*0.66=15.1 15th iteration: V [1] [2] =5.6*0.57=3.2 V [1] =1.6+1.3=2.9 V [1] [5] = 5.6*0.43=2.4 V [2] =3.2+3.7+2=8.9 V [2] [1] = 7.8*0.2=1.6 V [3] =2.8+3.3+2.9=9 V [2] [3] =7.8*0.36=2.8 V [4] =3.4 V [2] [4] =7.8*0.44=3.4 V [5] =2.4+4.5+2.9=9.8 V [3] [2] =15.6*0.24=3.7 V [6] =73+5.6=12.9 V [3] [5] =15.6*0.29=4.5 V [7] =1936.7+5.3+11.1=1953.1 V [3] [6] =15.6*0.47=7.3 V [4] [2] =7.3*0.27=2

67 ✓ [4] [7] =7.3*0.73=5.3 ✓ [5] [1] =10.2*0.13=1.3 ✓ [5] [3] =10.2*0.32=3.3 ✓ [5] [6] =10.2*0.55=5.6 ✓ [6] [3] =16.8*0.17=2.9 ✓ [6] [5] =16.8*0.17=2.9 ✓ [6] [7] =16.8*0.66=11.1 Total volume at (1, 2) =1536.1 Total volume at (1, 5) =1158.8 Total volume at (2,.1) =441.1 Total volume at (2, 3) =793.9 Total volume at (2, 4) =954.4 Total volume at (3, 2) =417.1 Total volume at (3, 5) =503.8 Total volume at (3, 6) =816.7 Total volume at (4, 2) =261.2 Total volume at (4, 7) =705.9 Total volume at (5, 1) =256.7 Total volume at (5, 3) =631.8 Total volume at (5, 6) =1085.8 Total volume at (6, 3) =321.3 Total volume at (6, 5) =321.3 Total volume at (6, 7) =1247.2 Actual total volume at each link after 15th iteration:

✓ (1, 2) =V [1] [2] - V [2] [1] =1536.1 - 441.1=1092 Similarly V (1, 5) = 902.1, V (2, 3) = 376.8, V (2, 4) = 693.2, V (3, 5) = -128, V (3, 6) =495.4, V (4, 7) = 705.9, V (5, 6) = 764.5, V (6, 7) = 1247.2

68 Fig 6.3 Calculated Traffic Volumes at each Link (15th iteration)

Finally the total volume calculated at each link is given as V(1, 2) = 1092, V (1, 5) = 908, V (2, 3) = 378, V (2, 4) = 715, V (3, 5) = -132, V (3, 6) =510, V (4, 7) = 715, V (5, 6) = 775, V (6, 7) = 1285 Step 5: Calculation of ratio of assigned volume and capacity of each link. R (1, 2) =V (1, 2) / C (1, 2) = 1092 / 3600 = 0.3 R (1, 5) =V (1, 5) / C (1, 5) = 908 / 1500 = 0.6 R (2, 3) =V (2, 3) / C (2, 3) = 378 / 3600 = 0.1 R (2, 4) =V (2, 4) / C (2, 4) = 715 / 3600 = 0.2 R (3, 5) =V (3, 5) / C (3, 5) = 132 / 1500 = 0.1 R (3, 6) =V (3, 6) / C (3, 6) = 510 / 3600 = 0.14 R (4, 7) =V (4, 7) / C (4, 7) = 715 / 3600 = 0.2 R (5, 6) =V (5, 6) / C (5, 6) = 775 / 1500 = 0.52

69 R (6, 7) =V (6, 7) / C (6, 7) = 1285 / 1000 = 1.285 Since for link (6, 7) the ratio of assigned volume to capacity is greater than 1. So the volume of each link recalculated by dividing the, assigned volume for each link by 1.285 and this link is assumed as redundant for next calculation. V (1, 2) = 850, V (1, 5) = 707, V (2, 3) = 294, V (2, 4) = 556, V (3, 5) = -103, V (3, 6) = 397, V (4, 7) = 557, V (5, 6) = 603, V (6, 7) = 1000

Fig 6.4 Readjusted Traffic Volumes at each Link

Remaining traffic distributed from 1 = 2000-1557=443

70 Step 6: Recalculate new shortest path by using 6-7 as redundant link.

Fig 6.5 Road Network and their Distance SP [1] = 2 + 1.5 + 1.8 = 5.3 SP [2] = 1.5 + 1.8 = 3.3 SP [3] = 1.5 + 1.5 + 1.8 = 4.8 SP [4] = 1.8 SP [5] = 1.6 + 1.5 + 1.5 + 1.8 = 6.4 SP [6] = 1.5 + 1.5 + 1.5 + 1.8 = 6.3 SP [7] = 0 Calculation of distance: Distance (1, 2) = 3.3 + 2 = 5.3 Distance (1, 5) = 6.4 + 4.5 = 10.9 Distance (2, 1) = 5.3 + 2 = 7.3 Distance (2, 3) = 4.8 + 1.5 = 6.3 Distance (2, 4) = 1.8 + 1.5 = 3.3 Distance (3, 2) =3.3 + 1.5 = 4.8 Distance (3, 5) = 6.4 + 1.6 = 8

71 Distance (3, 6) = 6.3 + 1.5 = 7.8 Distance (4, 2) = 3.3 + 1.5 = 4.8 Distance (4, 7) = 0 + 1.8 = 1.8 Distance (5, 1) = 5.3 + 4.5 =9.8 Distance (5, 3) = 4.8 + 1.6 = 6.4 Distance (5, 6) = 6.3 + 1.4 = 7.7 Distance (6, 3) =4.8 +1.5=6.3 Distance (6, 5) =6.4 + 1.4=7.8

Calculation of probability matrix: P (1, 2) = 0.67 P (1, 5) = 0.33 P (2, 1) = 0.23 P (2, 3) = 0.27 P (2, 4) = 0.50 P (3, 2) = 0.45 P (3, 5) = 0.27 P (3, 6) = 0.28 P.(4, 2) = 0.27 P (4, 7) = 0.73 P (5, 1) = 0.26 P (5, 3) = 0.41 P (5, 6) = 0.33 P (6, 3) = 0.55 P (6, 5) = 0.45

Calculation of volume at each link: 1St iteration: V [1] [2] = 443*0.67 = 296.8 V [2] =296.8 V [1] [5] = 443*0.33 = 146.2 V [5] = 146.2 2" iteration: V [2] [1] = 296.8*0.23 = 68.3 . V [1] = 68.3+38=106.3 V [2] [3] = 296.8*0.27 = 80.1 V [3] =80.1+60=140.1 V [2] [4] = 296.8*0.50 = 148.4 V [4] = 148.4 V [5] [1] = 146.2*0.26 = 38 V [6] = 48.2 V [5] [3] =146.2*0.41 = 60 V [5] [6] = 146.2*0.33=48.2 31-`1 iteration: V [1] [2] =106.3*0.67=71.2 V [2] =71.2+63+40.1=174.3 V [1] [5] =106.3*0.33=35.1 V [3] = 26.5 V [3] [2] =140.1*0.45=63 V [5] = 35.1+37.8+21.7=94.6

72 V [3] [5] —140.1*0.27-37.8 V [6] = 39.2 V [3] [6] =140.1*0.28=39.2 V [7] =108.3 V [4] [2] —148.4*0.27-40.1 V [4] [7] =148.4*0.73=108.3 V [6] [3] =48.2*0.55=26.5 V [6] [5] = 48.2*0.45=21.7 4th iteration: V [2] [1] = 174.3*0.23=40.1 V [1] =40.1+24.6=64.7 V [2] [3] =174.3*0.27=47.1 V [2] =12 V [2] [4] = 174.3*0.50-87.1 V [3] =47.1+38.8+21.6=107.5 V [3] [2] =26.5*0.45=12 V [4] =87.1 V [3] [5] = 26.5*0.27=7.2 V [5] =7.2+17.6=24.8 V [3] [6] =26.5 * 0.28 = 7.4 V [6] =7.4+31.2=38.6 V [5] [1] =94.6*0.26=24.6 V [7] =108.3 V [5] [3] = 94.6*0.41=38.8 V [5] [6] =94.6*0.33= 31.2 V [6] [3] =39.2*0.55=21.6 V [6] [5] =39.2*0.45=17.6 5th iteration: V [1] [2] =64,7*0.67=43.3 V [1] =2.8+6.4=9.2 V [1] [5] = 64.7*0.33=21.4 . V [2] =43.3+48.4+23.5=115.2 V [2] [1] =12*0.23=2.8 V [3] =3.2+10.2+21.2=34.6 V [2] [3] =12*0.27=3.2 V [4] =6 V [2] [4] =124'0.50=6 V [5] =21.4+29+17.4=67.8 V [3] [2] =107.5*0.45=48.4 V [6] =30.1+8.2=38.3 V [3] [5] =107.5*0.27=29 V [7] =108.3+63.6=171.9 V [3] [6] =107.5*0.28=30.1 V [4] [2] —87.1*0.27=23.5 V [4] [7] =87.1*0.73=63.6 V [5] [1] =24.8*0.26=6.4 V [5] [3] =24.8*0.41=10.2

73 V [5] [6] =24.8*0.33=8.2 V [6] [3] =38.6*0.55=21.2 V [6] [5] =38.6*0.45=17.4 6th iteration: V [1] [2] =9.2*0.67=6.2 V [1] =26.5+17.6=44.1 V [1] [5] = 9.2*0.33=3 V [2] =6.2+15.6+1.6=23.4 V [2] [1] =115.2*0.23=26.5 V [3] =31.1+27.8+21.1=80 V [2] [3] =115.2*0.27=31.1 V [4] =57.6 V [2] [4] =115.2*0.50=57.6 V [5] =3+9.3+17.2=29.5 V [3] [2] =34.6*0.45=15.6 V [6] =9.7+22.4=32.1 V [3] [5] =34.6*0.27=9.3 V [7] =171.9+4.4=176.3 V [3] [6] =34.6*0.28=9.7 V [4] [2] =6*0.27=1.6 V [4] [7] =6*0.73=4.4 V [5] [1] =67.8*0.26=17.6 V [5] [3] =67.8*0.41=27.8 V [5] [6] =67.8*0.33=22.4 V [6] [3] =38.3*0.55=21.1 V [6] [5] =38.3*0.45=17.2 7th iteration: V [1] [2] =44.1*0.67=29.5 V [1] =5.4+7.7=13.1 V [1] [5] = 44.1*0.33=14.6 V [2] =29.5+36+15.6=81.1 V [2] [1] =23.4*0.23=5.4 V [3] =6.3+12.1+17.7=36.1 V [2] [3] =23.4*0.27=6.3 V [4] =11.7 V [2] [4] =23.4*0.50=11.7 V [5] =14.6+21.6+14.4=50.6 V [3] [2] =80*0.45=36 V [6] =22.4+9.7=32.1 V [3] [5] =80*0.27=21.6 V [7] =176.3+42=218.3 V [3] [6] =80*0.28=22.4 V [4] [2] =57.6*0.27=15.6 V [4] [7] =57.6*0.73=42 V [5] [1] =29.5*0.26=7.7

74 ✓ [5] [3] =29.5*0.41=12.1 ✓ [5] [6] =29.5*0.33=9.7 ✓ [6] [3] =32.1*0.55=17.7 ✓ [6] [5] —32.1*0.45=14.4 8th iteration: V [1] [2] =13.1*0.67=8.8 V [1] =18.7+13.2=31.9 V [1] [5] = 13.1*0.33=4.3 V [2] =8.8+16.2+3.2=28.2 V [2] [1] =81.1*0.23=18.7 V [3] =21.9+20.7+17.7=60.3 V [2] [3] =81.1*0.27=21.9 V [4] =40.6 V [2] [4] =81.1*0.50-40.6 V [5] =4.3+9.7+14.4=28.4 V [3] [2] =36.1*0.45=16.2 V [6] =10.1+16.7=26.8 V [3] [5] =36.1*0.27=9.7 V [7] =218.3+8.5=226.8 V [3] [6] =36.1*0.28=10.1 V [4] [2] =11.7*0.27=3.2 V [4] [7] =11.7*0.73=8.5 V [5] [1] =50.6*0.26=13.2 V [5] [3] =50.6*0.41=20.7 V [5] [6] =50.6*0.33=16.7 V [6] [3] =32.1*0.55=17.7 V [6] [5] =32.1*0.45=14.4 9th iteration: V [1] [2] —31.9*0.67=21.4 V [1] =6.5+7.4=13.9 V [1] [5] = 31.9*0.33=10.5 V [2] =21.4+27.1+11=59.5 V [2] [1] =28.2*0.23=6.5 V [3] =7.6+11.6+14.7=33.9 V [2] [3] =28.2*0.27=7.6 V [4] =14.1 V [2] [4] =28.2*0.50=14.1 V [5] =10.5+16.3+12.1=38.9 V [3] [2] =60.3*0.45=27.1 V [6] =16.9+9.4=26.3 V [3] [5] =60.3*0.27=16.3 V [7] =226.8+29.6=256.4 V [3] [6] =60.3*0.28=16.9 V [4] [2] =40.6*0.27=11 V [4] [7] =40.6*0.73=29.6

75 [5] [1] =28.4*0.26=7.4 ✓ I ✓ [5] [3] =28.4*0.41=11.6 ✓ [5] [6] =28.4*0.33=9.4 ✓ [6] [3] =26.8*0.55=14.7 ✓ [6] [5] =26.8*0.45=12.1 10th iteration: V [1] [2] =13.9*0.67=9.3 V [1] =13.7+10.1=23.8 V [1] [5] = 13.9*0.33=4.6 V [2] =9.3+15.3+3.8=28.4 V [2] [1] =59.5*0.23=13.7 V [3] =16.1+15.9+14.5=46.5 V [2] [3] =59.5*0.27=16.1 V [4] =29.8 V [2] [4] =59.5*0.50=29.8 V [5] =4.6+9.2+11.8=25.6 V [3] [2] =33.9*0.45=15.3 V [6] =9.5+12.8=22.3 V [3] [5] =33.9*0.27=9.2 V [7] =256.4+10.3=266.7 V [3] [6] =33.9*0.28=9.5 V [4] [2] =14.1*0.27=3.8 V [4] [7] =14.1*0.73=10.3 V [5] [1] =38.9*0.26=10.1 V [5] [3] =38.9*0.41=15.9 V [5] [6] =38.9*0.33=12.8 V [6] [3] =26.3*0.55=14.5 V [6] [5] =26.3*0.45=11.8 11th iteration: V [1] [2] =23.8*0.67=15.9 V [1] =6.5+6.7=13.2 V [1] [5] =23.8*0.33=7.9 V [2] =15.9+20.9+8=44.8 V [2] [1] =28.4*0.23=6.5 V [3] =7.7+10.5+12.3=30.5 V [2] [3] =28.4*0.27=7.7 V [4] =14.2 V [2] [4] =28.4*0.50=14.2 V [5] =7.9+12.6+10=30.5 V [3] [2] =46.5*0.45=20.9 V [6] =13+8.4=21.4 V [3] [5] =46.5*0.27=12.6 V [7] =266.7+21.8=288.5 V [3] [6] =46.5*0.28=13 V [4] [2] =29.8*0.27=8

76 ✓ [4] [7] =29.8*0.73=21.8 ✓ [5] [1] =25.6*0.26=6.7 ✓ [5] [3] =25.6*0.41=10.5 ✓ [5] [6] =25.6*0.33=8.4 ✓ [6] [3] =22.3*0.55=12.3 ✓ [6] [5] =22.3*0.45=10 12th iteration: V [1] [2] =13.2*0.67=8.8 V [1] =10.3+7.9=18.2 V [1] [5] =13.2*0.33=4.4 V [2] =8.8+13.7+3.8=26.3 V [2] [1] =44.8*0.23=10.3 V [3] =12.1+12.5+11.8=36.4 V [2] [3] =44.8*0.27=12.1 V [4] =22.4 V [2] [4] =44.8*0.50=22.4 V [5] =4.4+8.2+9.6=22.2 V [3] [2] =30.5*0.45=13.7 V [6] =8.5+10.1=18.6 V [3] [5] =30.5*0.27=8.2 V [7] =288.5+10.4=298.9 V [3] [6] =30.5*0.28=8.5 V [4] [2] =14.2*0.27=3.8 V [4] [7] =14.2*0.73=10.4 V [5] [1] =30.5*0.26=7.9 V [5] [3] =30.5*0.41=12.5 V [5] [6] =30.5*0.33=10.1 V [6] [3] =21.4*0.55=11.8 V [6] [5] =21.4*0.45=9.6 13th iteration: V [1] [2] =18.2*0.67=12.2 V [1] =6+5.8=11.8 V [1] [5] =18.2*0.33=6 V [2] =12.2+16.4+6=34.6 V [2] [1] =26.3*0.23=6 V [3] =7.1+9.1+10.2=26.4 V [2] [3] =26.3*0.27=7.1 V [4] =13.2 V [2] [4] =26.3*0.50=13.2 V [5] =6+9.8+8.4=24.2 V [3] [2] =36.4*0.45=16.4 V [6] =10.2+7.3=17.5 V [3] [5] =36.4*0.27=9.8 V [7] =298.9+16.4=315.3 V [3] [6] =36.4*0.28=10.2 ✓ [4] [2] =22.4*0.27=6 ✓ [4] [7] —22.4*0.73=16.4 ✓ [51 Ell =22.2*0.26=5.8 , ✓ [5] [3] =22.2*0.41=9.1 ✓ [5] [6] =22.2*0.33=7.3 ✓ [6] [3] =18.6*0.55=10.2 V [6] [5] =18.6*0.45=8.4 14th iteration: V [1] [2] =11.8*0.67=7.9 V [1] =8+6.3=14.3 V [1] [5] =11.8*0.33=3.9 V [2] =7.9+11.9+3.6=23.4 V [2] [1] =34.6*0.23=8 V [3] =9.3+9.9+9.6=28.8 V [2] [3] =34.6*0.27=9.3 V [4] =17.3 V [2] [4] =34.6*0.50=17.3 V [5] =3.9+7.1+7.9=18.9 V [3] [2] =26.4*0.45=11.9 V [6] =7.4+8=15.4 V [3] [5] =26.4*0.27=7.1 V [7] =315.3+9.6=324.9 V [3] [6] =26.4*0.28=7.4 V [4] [2] =13.2*0.27=3.6 V [4] [7] =13.2*0.73=9.6 V [5] [1] =24.2*0.26=6.3 V [5] [3] =24.2*0.41=9.9 V [5] [6] =24.2*0.33=8 V [6] [3] =17.5*0.55=9.6 V [6] [5] =17.5*0.45=7.9 15th iteration: V [1] [2] =14.3*0.67=9.6 V [1] =5.4+4.9=10.3 V [1] [5] =14.3*0.33=4.7 V [2] =9.6+13+4.7=27.3 V [2] [1] =23.4*0.23=5.4 V [3] =6.3+7.7+8.5=22.5 V [2] [3] =23.4*0.27=6.3 V [4] =11.7 V [2] [4] =23.4*0.50=11.7 V [5] =4.7+7.8+6.9=19.4 V [3] [2] =28.8*0.45=13 V [6] =8.1+6.2=14.3 V [3] [5] =28.8*0.27=7.8 V [7] =324.9+12.6=337.5

78 ✓ [3] [6] =28.8*0.28=8.1 ✓ [4] [2] =17.3*0.27=4.7 ✓ [4] [7] —17.3*0.73-12.6 ✓ [5] [1] =18.9*0.26=4.9 ✓ [5] [3] =18.9*0.41=7.7 ✓ [5] [6] =18.9*0.33=6.2 ✓ [6] [3] =15.4*0.55=8.5 ✓ [6] [5] =15.4*0.45=6.9 The total traffic volume for 15 iteration is calculated as: V (1, 2) = 322.7, V (1, 5) = 106.7, V (2, 3) = -53.6, V (2, 4) = 349.2, V (3, 5) = -61.2, V (3, 6) = -14.9, V (4, 7) = 337.5, V (5, 6) = 29.2 Total resultant traffic volume at each link: V (1, 2) = 322.7 +850=1172.7, V (1, 5) = 106.7+707=813.7, V (2, 3) = -53.6+294=240.4, V (2, 4) = 349.2+556=905.2, V (3, 5) = -61.2-103=-164.2, V (3, 6) = -14.9+397=382.1, V (4, 7) = 337.5+557=894.5, V (5, 6) = 29.2 +603=632.2, V (6, 7) = 1000

Fig 6.6 Final Traffic Volumes at each Link (15 iteration)

79 6.3.2 Computer Analysis The same data is used in the developed software for multipath route assignment technique. The input data and pictorial view of output used in computer analysis shown in the module is shown below in the following screen prints.

MOT TIPAIT$ RotilT °A5,siGNM.Iffillt1 EMnor

Fig. 6.7 Screen Print of Entering No. of Node and No. of Link

80 :.*„...M.P.ttftekkagOgitr 4551„cOMENVIECIASZLIE Ve InPik Qutiva uelp"

NODE 70 20 2 90 40 3 so 60 4 100 60 5 uo 80 6 80 65 7 100 90

GSOM itit7k9.,*uat Fig. 6.8 Screen Print of Entering Coordinate of each Node

81 'Fik#441:-1;12ATY RainrASSIGN!AjM, TED;IN/SaP, Mut Wyk* ti

"ENTER LINK ANDD [STANCE / TRAVEL TIME

FROM NODE f TO NODE I TRAVEL TIME/DISTANCE

5 4.5 3t 1.5 4 1.5 5 1.5 6 1.5 7 1.9 6 1,4 7' 1

Fig. 6.9 Screen Print of Input of Travel time for each Link

82 NiULTIPATH ROUTE ASSItTRAKT • A .

NO, FROM NODE TO NODE CAPACITY

Fig. 6.10 Screen Print of Input of Link Capacity

83 L1 ,1 itcP71,Akslcislt,Aar,TCPISK „ 0.A ..J!ItttE Etlesutput'' Ii uelp_ '

ND; FROM NODE 1 , TO NODE r TRIP DISTRIBUTION 11 7:

RESULT I

Norton

Fig 6.11 Screen Print of Input of Traffic Flow from Origin to Destination

84 MIJLTIPATI1 ROUTg ASSititiONIT; tEttit;i1g14 ,

MDLTWATH-hOUTE ASSIGNMENT:

SHORTEST-PATH-DISTANCE 1.

DISTANCE

'PROBABILITY MATRIX . TRAFFIC•VOLUME

PICTORIAL VIEW

CAPACITY-RESTRAINED MULTI PATH ROUTE ASSIGNMENT:

SHORTEST PATH DISTANCE

TM DISTANCE

PROBABILITY MATRIX

TRAFF,I'C VOLUME

PICTORIAL VIEW -

EXIT

Nor to

Fig. 6.12 Screen Print of Result Module

85 gietATIf411-1 nouTS its-gc>N4W.T.E0B4R0 Ege 'mut Qutokit dan

PN 1 )=.' Sp( 2 )= SP( 6 )= 2.6 SP( 4 )= 1.8 SP( 6 )= 2.4 SP( 6 )= 1 SP( 7 )=1".1

Fig.6.13 Screen Print of Output of Shortest Path by Multipath Route Assignment Technique

86

14.41JPIR1173-1120111E, &SGN ENrtrCtIN I QL!E

CALCULATED DISTANCE OF EACH LINK:

Distance( 1, 2 )= 5.3 Distance( 1, 5 )= 6.9 Distance( 2, 1 )= 7.3 Distance( 2, 3 )= 4 Distance( 2, 4 )= 3.3 Distance( 3, 2 )= 4.8 Distance( 3, 5 )= 4 Distance( 3, 6 )= 2.5 Distance( 4, 2 )= 4.8 Distance( 4, 7 )=1.8 Distance( 5, 1 )= 9.8 Distance( 5, 3 ).-- 4.1 Distance( 5, 6 )= 2.4 Distance( 6, 3 )= 4 Distance( 6, 5.)= 3.8 Distance( 6, 7 )= 1

Fig.6.14 Screen Print of Output of Calculated Distance of each Link by Multipath Route Assignment Technique

87 ii4).4(11,:711?Alli ROUTE ASSIGNMENT-TECHNMUL:- ° • glOt

PROBABILITY MATRIX:

Pr(1, 2 ).7 0.57 Pr(1, 5)= 0.43 Pr( 2, 1 )= 0.2 Pr( 2, 3 )= 0.36 Pr( 2, 4 )= 0.44 Pr(.3, 2 )=- 0.24 Pr( 3, 5 )= 0.29 Pr( 3, 6 )= 0.47 Pr( 4. 2 )= 0.27 Pr( 4, 7 )= 0.73 Pr( 5, 1 )= 0.13 Pr(' 5.3)=)=. 0-32 Pr( 5, 6 )= 0.55 Pr( k )=. 0.17 Pr( 3, 5 )2= 0.17 Pr(3, 7 )= 036

Fig. 6.15 Screen Print of Output of Probability Matrix by Multipath Route Assignment Technique

88 MULtIPATH ROLITEASSIC;NIMENT 'TECHNIQUE' E.716" ; Input 'Cutout '

TRAFFIC VOLUME: V(1, 2 )= 1092 V( 1, ,5 ).= 908 V( 2, )=378 V( 2, 43=7.15 V( 3,5 ) -132 V(. 3, 6 )= 510 V( 4, 7 )=. 715 V( 5, 6 )= 775 V( 6, 7 )= 1285

Norton'

Fig.6.16 Screen Print of Output of Traffic Volume by Multipath Route Assignment Technique

89 MUKTIPAYFPROUTD FSSIGNIMEN17 TECIVIQUE, Eli': Input Qc■tput ter

•

PICTORIAL VIEW OF OUTPUT NETWORK

-start

Fig. 6.17 Screen Print of Pictorial View of Output by Multipath Route Assignment Technique

90 1.4 MULTIIIATIA 45,SIGNMENif 11:Ctit11:04?

SHORTEST PATH DISTANCE: SP( 1 )= 5.3 SP( 2 )= 3.8 SP( 3 )= 4.8 SP( 4 )= 1.8 SP( 5 )= 6.4 SP( 6 )= 6.3 SP(7)= 0

(6 Norton. QV'

Fig.6.18 Screen Print of Output of Shortest Path by Capacity Restraint Multipath Route Assignment Technique

91 A-MLIIKTIRATif ROUTE ASSIGNM NT TECHNIQOP -Ipput ',:Qn.tPut

CALCULA7MD DISTANCE OF'EACH LINK: Distance( 1, 2 )= 5.3 Distance('1, 5 )= 10.9 Distance( 2, 1 )= 7.3 Distance( 2; 3 )= 6.3 Distance( 2, 4 )= 3.3 Distance( 3, 2 )= 4.8 Distance(-3, 5 )= 8 Distance( 3, 6 )= 7.8 Distance( 4, 2 )= 4.8 Distance( 4, 7 )= 1.8 Distance( 5; 1 )=. 9.8 Distance(-5, 3.1= 6.4 DiStance( 5, 61= 7.7 Distance(6, 3 )= 6;3 Distance(6, 6 )= 7.8

ortorr

Fig.6.19 Screen Print of Output of Calculated Distance of each Link by Capacity Restraint Multipath Route Assignment Technique

92 4.1._t4 t11 • 455 lquArt4T-TraitIllaVr; • Die Input 2utPut LieltS

PROBABILITY MATRIX: Pr( 1, 2 )r-- 0.67 Pr( 1, 5 )-= 0.33 Pr( 2. 1 )= 0.23 Pr( 2, 3 ).= 0.27 Pr( 2.4 )= 0.51 Pr( 3, 2 )= 0.45 Pr( 3, 5-)= 0.27 Pr( 3, 6 )= 0.28 Prt 4. 2 Y.-- 027 Pr( 4, 7 ).7-- 0.73 Pr( 5, 1 )= 0.26 Pr( 5, 3 )=. 0.4 Pr( 5, 6 )= 0.33 Pr( 6, 3 )= 0.55 Pr( 6, 5 )-= 0.45

Fig. 6.20 Screen Print of Output of Probability Matrix by Capacity Restraint. Multipath Route Assignment Technique

93 w M4lrIPATKROUTF,f455iGriMINTITCHNIa1F,'°, Ege inaur tura

TRAFFIC VOLUME:

V( 1, 2 )= 1196 Traffic at Origin = 2000 V( 1, 5 )= 804 V( 2, 3 )= 197 Traffic at Destination = 1999 V( 2, 4 )= 999 V( 3, 5 )= -169 V( 3, 6 )= 366 V( 4, 7 )= 999 V( 5, 6 )=. 634 V( 6, 7 )= 1000

eitlaytpT..;

Fig.6.21 Screen Print of Output of Traffic Volume by Capacity Restraint Multipath Route Assignment Technique

94 3+3., ASSIGNt,404VTL'effNIQUE, ,

PICTORIAL. VIEW OF OUTPUT NETWORK

366 969

Fig. 6.22 Screen Print of Pictorial View of Output by Capacity Restraint Multipath Route Assignment Technique

95 6.4 COMPARISION OF RESULTS Table 6.2 traffic volume calculated data

Link : Traffic volume by manual Traffic volume by software calculation (15 iteration) (infinite iteration) Capacity Multipath Capacity Multipath restraint technique restraint technique , . multipath multipath technique technique 1-2 1172.7 1095 1196 1092 1-5 - 813.7 902.1 804 908 2-3 240.4 376.8 197 378 2-4 905.2 693.2 999 715 3-5 -164.2 -128 -169 132 3-6 382.1 495.4 366 510 4-7 894.5 705.9 999 715 5-6 632.2 764.5 634 775 6-7 1000 1247.2 1000 1285

The table 6.2 shows the traffic volume calculated at each link by manually and by developed software. On comparison of both result by manually and by developed software, it is found that both the result are about same. The little difference between results is due to less number of iteration in manual calculation. But in software, it is done until difference between traffic flow entering from origin and traffic reach at destination is equal to 0.01. If we do more and more iteration in manual calculation the result will becomes same as by software. It means developed software gives the same result as manually calculated. This comparison validates the software for giving true result as calculated manually for any road network. Thus the software can be used for route assignment for any road network.

96 CHAPTER-7

CONCLUSION AND RECOMMENDATION 7.1 CONCLUSIONS: Transportation planning involves so many iterative techniques, and large road networks, which is not possible to solve manually. Route assignment is the last phase of four stage transportation planning. Multipath route assignment technique seems to be the'most realistic among all those technique. This technique can be used in urban areas to solve the maximum of traffic problem. So, user friendly software for multipath route assignment technique has to be developed. The salient features of the-software are as follows: 1. Software has been developed in visual basic. 2. It is highly interactive and user-friendly. 3. It gives the output in text form and also in the form of pictorial view of output network. 4. It gives output for both the multipath route assignment technique and capacity restrained multipath route assignment technique. 5. The output of the software is shortest path, distance, probability matrix, traffic volume and pictorial view of output. 6. The help file included in the software help the user in how to use the software. 7. It is geographically transferable. 8. It gives accurate and quick result.

7.2 RECOMMENDATION: Research should continue to develop more efficient methods for solving complex assignment problems, such as stochastic network equilibrium, and to investigate the assumptions involved in the route-choice analysis.

97 REFERENCES

1. Bains, N.S. (2002), "Development of Software for Trip Assignment in Urban Areas", A Dissertation Report, I.I.T. Roorkee.

2. Chattraj, Ujjal (2003), "Development of software for multipath route assignment technique", A Dissertation Report, I.I.T. Roorkee.

3. Daganzo, Carlos F. (2002), "Reversibility of the time-dependent shortest path problem", Transportation Research Part B 36, pp. 665-668.

4. David E. Boyce, Der-Horng Lee, Bruce N. Janson, and Stainslaw Berka(1997), "Dynamic route choice model of large-scale traffic network", Journal of Transportation Engineering, vol. .123, No. 4, pp. 276-282.

5. Dial, R.B. (1970), "Probabilistic Assignment: A Multipath Traffic Assignment Model", Transportation Research, vol 5, no. 2, pp.83-111.

6. Easa, M. (1991), "Traffic Assignment in practice: Overview and Guidelines for Users", Journal of Transportation Engineering, vol. 117, No. 6, pp. 602-623.

7. Han, Sangin(2003), "Dynamic traffic modeling and dynamic stochastic user equilibrium assignment for general road networks", Transportation Research Part B 37, pp.225-249.

8. Hutchinson, B.G., "Route assignment analysis", Principle of Urban Transport Systems Planning, Mc Graw Hill Book Company, pp.122-147.

9. Jerry L. Edwards and Ferrol O. Robinson (1977), "Multipath Assignment Calibration for the Twin. cities", Journal of Transportation Engineering, vol. 103, No. TEC, pp. 791-806.

10. Kadiyali, L.R., "Traffic Assignment", Traffic Engineering and Transport Planning, Khanna Publishers, pp.699-705.

98 11. Kadiyali, L.R., "Trip Distribution", Traffic Engineering and Transport Planning, Khanna Publishers, pp: 640-645.

12. Kadiyali, L.R., "Transportation planning process", Traffic Engineering and Transport Planning, Khanna Publishers, pp. 634-637.

13. Khanna, S. K. and Justo, C. E. G., "Highway Engineering", 7th edition, Nemchand & Bros; Roorkee(Uttranchal), pp.1-3.

14. Konez Nicholas, Greenfield Joshua and Mouskos Kyriac (1996), "A strategy for solving static multiple-optimal-path transit network problems", Journal of Transportation Engineering, vol. 122, No. 3, pp.218-225.

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16. Maurya, A.K. (2000), "Short-Path software", A Mini Project Report, University of Roorkee.

17. Nielsen, Otto Anker (2000), "A stochastic transit assignment model considering differences in passengers utility functions", Transportation Research Part B 34, pp. 377-402.

18. Papacostas, C.S.,"Sequential Demand Forecasting Models", Fundamentals of Transportation Engineering, Prentece-Hall Publishers, pp.245-302.

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99 21. Ridwan, M. (2004), "Fuzzy preference based traffic assignment problem", Transportation Research part C 12, pp.209-233.

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100 APPENDIX SOURCE CODE OF THE SOFTWARE "MULTIPATH ROUTE ASSIGNMENT TECHNIQUE" Frm co ordinate Private Sub cmdNextClick() filuDataEntry.Show End Sub Private Sub Form Load() Dim I As Integer frmCoordinate.Width = Screen.Width frmCoordinate.Height = Screen.Height - 1200 frmCoordinateleft = 0 fnnCoordinate.Top = 1200 Gridl.Width = 4500 Gridl.Height = funCoordinate.Height / 2 Gridl.Top = 1000 Gridl .Left = 1000 Labe13.Top = 500 Labe13.Left = 1000 cmdNext.Left = 6000 cmdNext.Top = frmCoordinate.Height - 6000 Grid! .ColWidth(0) = 600 Gridl.ColWidth(1) — 1200 • Gridl.ColWidth(2) = 1200 Gridl.ColWidth(3) = 1200 For I = 1 To Gridl .Rows - 1 Grid1.TextMatrix(I, 0) = I Next Gridl.FixedAlignment(0) = 4 Gridl.TextMatrix(0, 0) = "NO." Gridl.FixedAlignment(1) = 4

101 Gridl.TextMatrix(0, 1) = "NODE" Gridl.FixedAlighinent(2) = 4 Gridl.TextMatrix(0, 2) = "X" Gridl.FixedAlignment(3) = 4 Gridl.TextMatrix(0, 3) = "Y" Gridl .Row = 1 Gridl.Col = 1 SetTextbox End Sub Private Sub Gridl EnterCell() ' Make sure the user doesn't attempt to edit the fixed cells If Gridl .MouseRow = 0 Or Gridl.MouseCol = 0 Then Textl .Visible = False Exit Sub End If ' clear contents of current cell Textl .Text = "" ' place Textbox over current cell Textl .Visible = False Textl .Top = Gridl .Top + Gridl,CellTop Textl.Left = Gridl.Left + Gridl.CellLeft Textl.Width = GridI.CellWidth Textl.Height = Gridl.CellHeight ' assing cell's contents to Textbox Textl .Text = Gridl.Text ' move focus to Textbox Text1.Visible = True Textl.SetFocus End Sub Private Sub Gridl LeaveCell() Gridl.Text = Textl.Text

102 End Sub Private Sub Textl KeyPress(KeyAscii As Integer) If KeyAscii = 13 Then If Gridl.Col = Gridl .Cols - 1 Then If Gridl.Row = Gridl.Rows - I Then Exit Sub Else Gridl.Row = Gridl.Row + 1 End If Gridl.Col = 1 Else Gridl.Col = Gridl.Col + 1 End If End If End Sub Sub SetTextbox() Textl .Visible = False Textl .Top = Gridl .Top + Gridl.CelITop Textl.Left = Gridl.Left + Gridl.CellLeft Textl.Height = Gridl.CellHeight Textl.Width = Gridl.CellWidth Textl .Text = Gridl.Text Textl .Visible = True End Sub Frmdata Private Sub cmdNextCIick() frmCoordinate.Show End Sub Private Sub Form Load() frmData.Width = Screen. Width L illy ata.Height = Screen.Height - 1200

103 frmData.Left = 0 frmData.Top = 1200 cmdNext.Left = 5000 cmdNext.Top = 5000 Labe11.Top = 1500 Labell .Left = 1000 Labe12.Top = 2500 Label2.Left = 1000 Textl.Top = 1500 Textl .Left = 4000 Text2.Top = 2500 Text2.Left = 4000 Picture1.Height = 4500 Picture 1 .Width = 6400 Picturel.Top = 1000 Picturel left = 7000 End Sub Frmdataentry Private Sub cmdNext_Click0 frniTripDist.Show End Sub Private Sub Form Load() Dim I As Integer frmDatoEntry. Width = Screen. Width frmDataEntry.Height = Screen.Height - 1200 frmDataEntry.Left = 0 frmDataEntry.Top = 1200 cmdNext.Left = 9000 cmdNext.Top = IlmDataEntry.Height - 5000 Gridl.Width = 7700 Gridl.Height = frmDataEntry.Height / 2 + 1000

104 Gridl .Top = 1000 Gridl .Left = 1000 Labell .Left = 1000 Labell .Top = 500 Gridl .ColWidth(0) = 600 For I = 1 To Gridl .Rows - 1 Grid1.TextMatrix(I, 0) = I Next For I = 1 To 3 Grid I .ColWidth(I) = 2200 Next Gridl.FixedAlignment(0) = 4 Gridl.TextMatrix(0, 0) = "NO." Gridl.FixedAligriment(1) = 4 Gridl .TextMatrix(0, 1) = "FROM NODE" Gridl.FixedAlignment(2) = 4 Gridl.TextMatrix(0, 2) = "TO NODE" Gridl.FixedAlignment(3) = 4 Gridl.TextMatrix(0, 3) = "TRAVEL TIME/DISTANCE" Gridl .Row = 1 Gridl.Col = 1 SetTextbox End Sub Private Sub Gridl EnterCell() ' Make sure the user doesn't attempt to edit the fixed cells If Gridl.MouseRow = 0 Or Gridl.MouseCol = 0 Then Textl.Visible = False Exit Sub End If ' clear contents of current cell Textl.Text = ""

105 ' place Textbox over current cell Text 1 .Visible = False Textl.Top = Gridl.Top + Gridl.CellTop Textl .Left = Gridl .Left + Gridl.CellLeft Textl.Width = Gridl.CellWidth Textl.Height = Gridl.CellHeight assing cell's contents to Textbox Textl.Text = Gridl.Text ' move focus to Textbox Textl .Visible = True Textl.SetFocus End Sub Private Sub Gridl LeaveCell() Gridl.Text = Textl.Text End Sub Sub SetTextbox() Textl.Visible — False Textl.Top = Gridl.Top + Grid1.CellTop Textl .Left = Gridl.Left + Gridl..CellLeft Textl .Height = Gridl.CellHeight Textl.Width = Gridl.CellWidth Textl.Text = Gridl.Text Text 1 .Visible = True End Sub Private Sub Textl KeyPress(KeyAscii As Integer) If KeyAscii = 13 Then If Gridl.Col Grid 1 .Cols - 1 Then If Gridl.Row = Gridl.Rows - 1 Then Exit Sub Else Gridl.Row = Gridl.Row + 1

106 End If Gridl.Col — 1 Else Grid 1 .Col = Grid 1 .C91 + 1 End If End If End Sub Frmtrip Private Sub Form Load() Dim I, od As Integer frmtrip.Width = Screen.Width frmtrip.Height = Screen.Height - 1200 frmtrip.Left 0 frmtrip.Top = 1200 Gridl.Width = 7600 Gridl.Height = 2500 Gridl.Top = 2500 Gridl left = 1000 Label' Left — 1000 Labell.Top — 2000 Labell .Width = 3000 Label2.Left — 1000 Labe12.Top = 1000 Label2.Width = 5500 Text2.Left = 6000 Text2.Top = 1000 Text2.Width = 1200 Text2.Height = 500 cmdNext.Left = 8000 cmdNext.Top = 5500 Gridl.ColWidth(0) = 600

107 For I = 1 To 50 Gridl.TextMatrix(I, 0) = I Next For I = 1 To 3 Gridl.ColWidth(I) = 2200 Next Gridl.FixedAlignment(0) = 4 Gridl.TextMatrix(0, 0) = "NO." Gridl.FixedAlignment(1) = 4 Gridl .TextMatrix(0, 1) = "FROM NODE" Gridl.FixedAlignment(2) = 4 Gridl.TextMatrix(0, 2) = "TO NODE" Gridl.FixedAlignment(3) = 4 Gridl.TextMatrix(0, 3) = "TRIP DISTRIBUTION" Gridl .Row = 1 Grid 1 .Col = 1 SetTextbox End Sub Private Sub Gridl EnterCe110 ' Make sure the user doesn't attempt to edit the fixed cells If Gridl.MouseRow = 0 Or Gridl.MouseCol = 0 Then Textl.Visible = False Exit Sub End If ' clear contents of current cell Textl .Text = "" ' place Textbox over current cell Textl.Visible = False Textl .Top = Grid1.Top + Grid 1 .CellTop Textlieft = Gridl .Left + Gridl .CellLeft Textl .Width = Gridl.CellWidth

108 Textl .Height = Gridl.CellHeight ' assing cell's contents to Textbox Textl.Text = Gridl.Text ' move focus to Textbox Textl.Visible = True Textl.SetFocus End Sub Private Sub Gridl LeaveCell() Gridl.Text = Textl.Text End Sub Sub SetTextbox() Text 1 .Visible = False Textl. Top = Gridl.Top + Gridl.CellTop Textl .Left = Grid 1 .Left + Gridl .CellLeft Textl .Height = Gridl.CellHeight Textl . Width = Grid 1 .CellWidth Textl.Text = Gridl.Text Text! .Visible = True End Sub Private Sub Text 1 KeyPress(KeyAscii As Integer) If KeyAscii = 13 Then If Gridl.Col = Gridl . Cols - 1 Then If Gridl.Row = Gridl.Rows - 1 Then Exit Sub Else Gridl.Row = Gridl.Row + 1 End If Gridl.Col = 1 Else Gridl.Col = Gridl.Col + 1 End If

109 End If End Sub Frmtripdist Private Sub Form Load() Dim I As Integer frmTripDist.Width = Screen.Width fiiiTripDist.Height = Screen.Height - 1200 funTripDistleft = 0 frmTripDist.Top = 1200 Gridl.Width = 7100 Grid 1 .Height = frmTripDist.Height / 2 GridI.Top = 1500 Grid1 left = 1000 Label 1 .Left = 1000 Labell .Top = 1000 Commandl .Top = 2800 Command 1 .Left = 9000 Gridl.ColWidth(0) = 600 For I = 1 To 3 Grid1.ColWidth(I) = 2000 Next I For I = 1 To Gridl .Rows - I Gridl.TextMatrix(I, 0) = I Next Grid1.FixedAlignment(0) = 4 Gridl.TextMatrix(0, 0) = "NO." Gridl.FixedAlignment(1) = 4 Gridl.TextMatrix(0, 1) = "FROM NODE" Grid1.FixedAlignment(2) = 4 Gridl.TextMatrix(0, 2) = "TO NODE" Gridl.FixedAlignment(3) = 4

110 Gridl.TextMatrix(0, 3) = "CAPACITY" Gridl.Row.= 1 Gridl .Col = 1 SetTextbox End Sub Output Private Sub Commandl Click() frmGraphics. Show Dim I, j, k, od, templ, temp2 As Integer Dim link, node, perl(50), per2(50) As Integer Dim D(50), C(50, 50), c3(50), max2, max3, mini, min2 As Double Dim X(50), Y(50), cl(50), c2(50) As Integer Dim v(50, 50), m(50, 50), v1(20, 20, 20), r(50, 50) As Double Dim z1(50), z2(50), z3(50), nodeXlabel(50) As Integer Dim x1(50), yl (50), x2(50),: y2(50) As Integer Dim nodesum(50), nodeYlabel(50), 1(50, 50), 11(50), 12(50, 50) As Double Dim d1(50, 50), d2(50), d3(50), R1(50), R2(50), R3(50) As Double Dim v2(50, 50,',:$0), SP(50), dist(50, 50) As Double Dim pr(50, 50), tt(50), u3(50), b(20), p(50, 50), ul (50) As Double Dim t1(50, 50), t(50, 50), MF(50, 50), maxi, u2(50), v3(50, 50; 50) As Double Dim spl(50), distl(50, 50), d4(50, 50), d5(50), d6(50), prl (50, 50) As Double Dim V4(50, 50, 50), v5(50, 50, 50) As Double Dim v6(50, 50, 50), u4(50), vo, vn, vol, vnl, vo2, vn2 As Double Dim maxX, maxY, minX, minY, mx, my, scale 1, scale2, scale3 As Double Dim m1(50), n1(50), pl(50), q1(50), p2(50, 50) As Double Dim infinity As Currency infinity = 999999999999# link = CInt(finiData.Text2.Text) node = CInt(frmData.Textl.Text) For I = 1 To 49 zl(I) = Val(frmCoordinate.Gridl.TextMatrix(I, 1))

111 z2(I) = Val(funCoordinate.Gridl.TextMatrix(I, 2)) z3(I) = Val(funCoordinate.Grid1.TextMatrix(I, 3)) cl(I) = Val(fauTripDist.Gridl.TextMatrix(I, 1)) c2(I) = Val(frinTripDist.Grid1.TextMatrix(I, 2)) c3,(I) = Val(frmTripDist.Grid1.TextMatrix(I, 3)) X(I) = Val(frmDataEntry.Gridl.TextMatrix(I, 1)) Y(I) = Val(filliDataEntry.Gridl.TextMatrix(I, 2)) 11(I) = Val(filliDataEntry.Gridl.TextMatrix(I, 3)) Next od = Val(frmtrip.Text2.Text) 'distance between node i and j For k = 1 To link For I = 1 To node For j = 1 To node If (X(k) = I And Y(k) = j) Then 1(I, j) = 11(k) 1(j, I) =1(I, j) End If Next j Next I Next k For I = 1 To od perl(I) = frmtrip.Gridl.TextMatrix(I, 1) per2(I) = frmtrip.Gridl.TextMatrix(I, 2) b(I) = flintrip.Gridl.TextMatrix(I, 3) Next 'capacity and volume between node i and j For k = 1 To 49 For I = 1 To node For j = 1 To node If (cl(k) — I And c2(k) j) Then

112 C(I, j) = c3(k) End If Next j Next I Next k ' calculation 'calculation of shortest path from i to destination node

For I = 1 To node For j = 1 To node If l(I, j) = 0 Then m(I, j) = infinity Else m(I, j) = 1(I, j) End If Next j Next I For k = 1 To node For I = 1 To node For j = 1 To node If m(I, j) < m(I, k) + m(k, j) Then m(I, j) = m(I, j) Else m(I, j) k) + m(k, j) End If Next j Next I Next k For I = 1 To node SP(I) = m(I, node) SP(node) = 0

113 Next For I = 1 To node - 1 For j = 1 To node If Not 1(1, j) = 0 Then dist(I, j) = SP(j) + 1(I, j) Else dist(I, j) = 0 End If Next j Next I For I = 1 To node - 1 For j = 1 To node If Not dist(I, j) = 0 Then d 1(I, j) = 1 / dist(I, j) End If Next j Next I For I = 1 To node - 1 d2(I) = 0 Next I For I = 1 To node - 1 For j = 1 To node If Not 1(I, j) = 0 Then d2(I) = d2(I) + d 1 (I, j) d3 (I) = 1 / d2(I) End If Next j Next I For I = 1 To node - 1 For j = 1 To node If Not 1(1, j) = 0 Then

114 pr(I, j) = d3(I) * dl (I, j) End If Next j Next I

'calculation of volume For k = 1 To od For I = 1 To node For j = 1 To node vl (k, I, j) = 0 Next j Next I Next k For I = 1 To node For j = 1 To node p(I, j) = 0 Next j Next I For I = 1 To node u(I) = 0 Next For k = 1 To od temp 1 = perl(k) temp2 = per2(k) u(templ) = b(k) Do For I = 1 To node If Not I = temp2 Then For j = 1 To node If Not pr(I, j) = 0 Then p(I, j) = u(I) * pr(I, j)

115 Else: p(I, j) = 0 End If u(j) = u(j) + p(I, j) If I < j Then vl(k, I, j) = vl(k, I, j) + p(I, j) Else vl(k, I, j) = vl(k, I, j) - p(I, j) End If = 9 Next j u(I) = 0 End If Next I Loop While ((u(temp2) - b(k)) > 0.01 Or (b(k) - u(temp2)) > 0.01) vol = b(k) vnl = u(temp2) For I = 1 To node For j = 1 To node v2(k, I, j) = vl(k, I, j) + vl(k, j, I) Next j Next I For I = 1 To node For j = 1 To node If Not dist(I, j) = infinity Then If I < j Then If (v2(k, I, j) - Int(v2(k, I, j))) >= 0.5 Then v2(k, I, j) = Int(v2(k, I, j)) + 1 Else v2(k, I, j) = Int(v2(k, I, j)) End If Else

116 v2(k, I, j) = 0 End If End If Next j Next I

For I = 1 To node For j = 1 To node If Not v2(k, I, j) = 0 And I < j And Not C(I, j) = 0 Then MF(I, j) = v2(k, I, j) / C(I, j) End If Next j Next I For I = 1 To node For j = 1 To node If MF(I, j) > 1 Then MF(I, j) = MF(I, j) Else: MF(I, j) = 1 End If Next j Next I maxi =0 For I = 1 To node For j = 1 To node If max3 < MF(I, j) Then max3 = MF(I, j) End If Next j Next I For I = 1 To node For j 1 To node

117 If I < j Then v2(k, I, j) = v2(k, I, j) / max3 End If If (v2(k, I, j) - Int(v2(k, I, j))) >= 0.5 Then v2(k, I, j) = Int(v2(k, I, j)) + 1 Else v2(k, 1, j) = Int(v2(k, 1, j)) End If Next j Next For I = 1 To node For j = 1 To node If MF(I, j) > 1 Then v3(k,I,j)=0 Else: v3(k, I, j) = v2(k, I, j) End If Next j Next I u1(1)= 0 For j = 1 To node u1(1) = u1(1) + v2(k, 1, j) ul(node) = ul (node)-+ v2(k, j, node) Next u2(l) = b(k) - u1(1) For I = 1 To node For j = 1 To node If Not v3(k, I, j) = 0 Then j) —1(I, j) Else: 1(I, j) = 0 End If Next j

118 Next I For I = 1 To node For j = 1 To node 10, I) = l(I, j) Next j Next I Next k

'calculation of shortest path For I = 1 To node For j = 1 To node If 1(I, j) = 0 Then m(I, j) = infinity Else m(I, j) l(I, j) End If Next j Next I For k = 1 To node For I = 1 To node For j = 1 To node If m(I, j < m(I, k) + m(k, j) Then m(I, j) = m(I, j) Else m(I, j) = m(I, k) + m(k, j) End If Next j Next I Next k For I = 1 To node spl (I) = m(I, node)

119 spl(node) = 0 Next For I = 1 To node - 1 For j = 1 To node If Not 1(I, j) 0 Then distl(I, j) = spl (j) + j) Else distl (I, j) = 0 End If Next j Next I For I = 1 To node - 1 For j = 1 To node If Not distl(I, j) = 0 Then d4(I, j) = 1 / distl(I, j) End If Next j Next I ForIW 1 To node - I d5(I) = 0 Next I For I = 1 To node - 1 For j = 1 To node If Not 1(I, j) = 0 Then d5(I) = d5(I) + d4(I, j) d6(I) = 1 / d5(I) End If Next j. Next I For I = 1 To node - 1 For j = 1 To node

120 If Not 1(I, j) = 0 Then prl (I, j) = d6(I) * d4(I, j) End If Next j Next I

'calculation of trip by capacity restraint For k = 1 To od For I = 1 To node For j = 1 To node V4(k, I, j) = 0 Next j Next I Next k For I = 1 To node For j = 1 To node p2(I, j) = 0 Next j Next I For I = 1 To node u3 (I) = 0 Next For k = 1 To od temp I = perl(k) temp2 = per2(k) u3(1)= u2(1) Do For I = 1 To node If Not I = temp2 Then For j = 1 To node If Not pr 1 (I, j) = 0 Then

121 p2(I, j) = u3(I) * prl (I, j) Else: p2(I, j) = 0 End If u3(j) = u3(j) + p2(I, j) If I < j Then V4(k, I, j) = V4(k, I, j) + p2(I, j) Else V4(k, I, j) = V4(k, I, j) - p2(I, j) End If p2(I, j) = 0 Next j u3(I) = 0 End If Next I Loop While ((u2(1) - u3(temp2)) > 0.01 Or (u3(temp2) - u2(1)) > 0.01) vo2 = u2(1) vn2 = u3 (temp2) For I = 1 To node For j = 1 To node v5(k, I, j) = V4(k, I, j) + V4(k, j, I) Next j Next I For I = 1 To node For j = 1 To node If Not dist I (I, j) = infinity Then If I < j Then If (v5(k, I, j) - Int(v5(k, I, j))) >= 0.5 Then v5(k, I, j) = Int(v5(k, I, j)) + 1 Else v5(k, I, j) = Int(v5(k, I, j)) End If

122 Else v5(k, I, j) = 0 End If End If Next j Next I Next k For k = 1 To od For I = 1 To node For j = 1 To node v6(k, I, j) = v2(k, I, j) + v5(k, I, j) Next j Next I Next k vo = u1(1) + vo2 vn = ul (node) + vn2 If (vn Int(vn)) >= 0.5 Then vn = Int(vn) + 1 Else vn = Int(vn) End If maxl = 0 max2 = 0 minl =0 min2 = 0 For I = 1 To node If maxl < z2(I) Then maxi = z2(I) End If Next For I = 1 To node

123 If mini > z2(I) Then mint = z2(I) End If Next For I = 1 To node If max2 < z3 (I) Then max2 = z3(I) End If Next For I = 1 To node If min2 > z3(I) Then min2 = z3(I) End If Next maxX = max 1 maxY = max2 minX = mini minY = min2 mx = frmGraphics.Width - 3000 my = frmGraphics.Height - 3000 scale 1 = mx / (maxX - minX) scale2 = my / (maxY minY) If (scale 1 < scale2) Then scale3 = scale 1 Else scale3 = scale2 End If For = 1 To node z2(I) = scale3 * z2(I) z3(I) = scale3 * z3(I) Next

124 For I = 1 To node For j = 1 To link If X(j) = zl(I) Then m 1 (j) = z2(I) nl(j) = z3(I) End If Next j Next I For I = 1 To node For j = 1 To link If Y(j) = zl(I) Then pl(j) = z2(I) ql (j) = z3(I) End If Next j Next I frmGraphics.FontSize = 14 For j = 1 To link frmGraphics.Line (m I (j), n1(j))-(p1(j), q1(j)), QBColor(2) Next For I = 1 To node frmGraphics.Circle (z2(I), z3(I)), 250, QBCoIor(1) Next For I = 1 To node frmGraphics.CurrentX = z2(I) - 135 frmGraphics.CurrentY = z3(I) - 200 frmGraphics.Print Next For I = 1 To node For j = 1 To node If Not v2(1, I, j) = 0 Then frmGraphics.CurrentX = (z2(I) + z2(j)) / 2 - 300 frmGraphics.CurrentY = (z3(I) + z3(j)) / 2 - 100 funGraphics.Print CDbI(v6(1, I, j)) End If Next j Next I frmGraphics.CurrentX = 5000 frmGraphics.CurrentY = 200 frmGraphics.Print "PICTORIAL VIEW OF OUTPUT NETWORK" frmGraphics.CurrentX = 5000 frmGraphics.CurrentY = 400 frmGraphics.Print "

End Sub