22 TRANSPORTATION RESEARCH RECORD 1162 Characteristics of Metro Networks and Methodology for Their Evaluation ANTONIO Musso AND VuKAN R. VucH1c PURPOSE, ORGANIZATION, AND SCOPE Presented In this paper are the results of research on metro (rapid transit) networks, focusing on their geometric charac­ teristics. The object Is to define the most important measures, Presented in this paper is a systematic set of quantitative Indicators, and characteristics of geometric forms that can elements that defines the network characteristics of metro sys­ Improve the present predominantly empirical methods used in tems that can be used for their description, evaluation, and metro network planning and analysis. Several measures of comparative analysis. Examples of such evaluations include metro network size and rorm, including length, number or planning of new or analysis of existing networks, their com­ lines, and stations, which express the extensiveness of the sys­ parison with networks of other cities, and comparison of alter­ tem, are selected; they are also needed for derivations of various indicators. A number of selected indicators are then native network extensions. presented. These represent the most effective tool for network The quantitative elements are grouped into five general cate­ comparison because most of them are Independent of network gories, as follows: size. Several Indicators relating metro network to the city size and population express the degree of adequacy of the network 1. Measures of network size and form, to meet the city's needs. Based on experiences from a number of metro systems, characteristics of different types of lines 2. Indicators of network topology, (radial, diametrical, circumferential, and other) are defined. 3. Measures of relationship between network and city, These allow evaluation of network types, such as radial-cir­ 4. Quantity and quality of offered service, and cumferential versus grid networks. An analysis of metro net­ 5. Measures of service use. works in 10 different cities is presented to Illustrate the ap­ plications of theoretical and empirical materials; several basic measures and indicators of these networks have been com­ The sections covering these five categories are follo\ved by a puted and analyzed. The scope of quantitative elements, analy­ description of the basic forms of metro lines and their charac­ ses of types of lines, and descriptions of networks are limited teristics. Finally, an application of these measures to metro because of space constraints, but they illustrate the methodol­ networks in 10 cities is given using many of the elements ogy that can be used, In a more comprehensive way, for a defined previously. number of different analyses of metro networks, their designs, Many different aspects of metro networks can be analyzed; or their extensions. the emphasis here is on the geometric form and the method of operation of transit lines and networks; that is, on categories The planning of metro (rapid transit) networks is usually pre­ 1-3 listed. Categories 4 and 5 are given only as a guideline for dominantly empirical. Consideration of local conditions, such analysis focusing on service quality and efficiency of as demand characteristics, existence of transportation corridors, operations. requirements for certain station locations, and so on, tend to In this paper, theoretical concepts are selectively used, par­ suppress the analyses of network topology and geometric ticularly from graph theory (J), focusing on those with practi­ characteristics. However, even though designers of metro lines cal relevance to actual metro network planning. The paper is and networks may want to use some design guidelines, to also based on experiences from many cities on metro network perform comparative analyses or to make use of experiences design, service, and operating characteristics. from network operations in other cities, very few of these can be found in the professional literature. As already mentioned, the data needed for network planning Because of the high cost of metro construction and the and analysis vary with the purpose of the analysis and local permanence of its facilities, it is important to design optimal conditions in the city studied. The data used for the indicators networks with respect to service for passengers, efficiency of and analyses presented in this paper are listed in Table 1. operation, and relationship of the metro system to the city. This is a complex task and it deserves more attention than it has MEASURES AND INDICATORS OF received until now. An attempt is made in this study to provide METRO NETWORKS materials that may assist in the planning and design of metro system networks, lines, and stations. Network Size and Form A. Musso, Department of Civil Engineering, University of Salemo, Salemo, Italy. Current address: 15, Via Domenico Cirillo, 00197 The main elements that express the size and form of a metro Rome, Italy. V. R. Vuchic, University of Pennsyivania, Department of network arc defined as follows. Corresponding terms from Systems, 113 Towne Building, Philadelphia, Pa. 19104-6315. graph theory are given in parentheses. Musso and Vuchic 23 TABLE 1 BASIC INFORMATION NEEDED FOR METRO LINE NIJM8ER NETWORK ANALYSIS I @ MULTIPLE STATIONS Number Item Symbol Dimension J 2 2 2 1 Population of the served area p Persons 2 2 Surface of the served area Su km ® I 2 2 MLt.TIPLE SFflCINO{k,2) J SPACING LENGTH 3 Vehicle-km operated per day w veh-km (km) 4 Vehicle or car capacity Cv Spaces/veh 5 Vehicles per train [transit unit a ILLUSTRATION OF NETWORK ELEMENTS (TU)] nru vehffU 6 Operating speed Vo km/h ® ..-- -CD 7 Frequency of service f TU/h 8 Number of metro passengers per day Pad Persons/day 9 Number of metro passengers per year ~ay Persons/year 10 Average trip length Ip km 11 Number of total transit passengers per day P, Persons/day b ELEMENTS FOR COMPUTATION OF 00 VALUES 12 Number of stations on the FIGURE 1 Network schematics. network N Stations 13 Number of stations with park-and-ride NP Stations a-7 Number of station spacings in a network, A, is computed 14 Schematic map of network as the sum of spacings on individual lines minus the multiple with stations spacings, as explained under a-4: 15 Number of lines and their lengths n1, Ii -,km n1 kmu A = I. ai - I. k x a~ (3) i=l k=2 a-1 Number of stations (nodes) on a line i, ni. This number can also be computed via N: a-2 Number of interstation spacings (arcs) on a line i, ai, is related to n as follows: A= N- 1 + C, (4) (1) where C, is the number of closed circles in the network. In the a-3 Length of line i, li. case illustrated in Figure la, the number of spacings (including a-4 Number of multiple stations (jointly used by two or more single and multiple) computed by line is lines), n~. and lengths of double sections, t!. in which k designates the number of lines using a station or a spacing. These superscripts must be introduced to avoid double count­ A = 7 + 8 + 3 - (1 x 3 + 2 x 1) = 13 spacings ing in computations of the number of stations, spacings, and origin-destination (OD) pairs. For these computations the num­ Alternatively, using the number of stations (Equation 4), the ber of stations, n~, must be computed as 1 less than the number number of spacings is of lines it serves (i.e., as k - 1, while the number of multiple spacings, a~. and their lengths, l~. are used as given). This will A = 13 - 1 + 1 = 13 spacings be illustrated on cases following a-6, a-7, and a-8. a-5 Number of lines in a network, n • 1 a-8 Length of network, L, is the sum of line lengths minus a-6 Number of stations in a network, N, is computed as the the multiple spacings: sum of stations on individual lines minus the multiple stations as follows: n1 kmax ni kmu L = I. Ii - I. (k - 1) x l~ (5) i=l k=2 N = I. ni - I. (k - 1) x n~ (2) i=l k=2 Using the example from Figure la: For example, the network in Figure la consists of three lines with 8, 9, and 4 stations, respectively: L = 12 + 14 + 5 - (1 x 1 + 2 x 2 + 1 x 1 + 1 x 2) = 23 km 2 3 nm = 4 and nm = 2 a-9 Number of circles in a network, c,.. The number of thus, the total number of stations (single and multiple) in the circles in a network can be computed by Equation 4 as: network is N = 8 + 9 + 4 - (1 x 4 + 2 x 2) = 13 stations C, =A - N + 1 (6) 24 TRANSPORTATION RESEARCH RECORD ll62 The range of Cr values is 0 < Cr < 2N - 5. N = 6 + 7 + 8 - (4 x 1 + 1 x 2) = 15 stations a-10 Number of station-to-station travel paths, OD, consists OD = 1/z x 15 (15 - 1) = 105 paths of direct paths, ODd, and paths that include one or more transfers, OD1• In a network with N stations, the number of all The computation of ODd now becomes more complex. The possible OD paths is first sum in Equation 9 is: OD = N (N - 1)/2 (7) ,., (1/2) L. ni(ni - 1) =( 1/z) x (6 x 5 + 7 x 6 + 4 x 3) For a line with i stations, the number of OD paths is i=l = 42 paths (8) the last member (4 x 3) representing the branch section e-h. and all of them are direct. The total number of direct paths in a The second sum from Equation 9 must include the additional network is equal to the sum of OD paths along each line and paths between stations: a-band d-e (2 x 2), a-d aml/-h (4 x along each single branch plus the paths on overlapping lines 3); thus, (i.e., those serving jointly sections of different lines): "d ODd = 1/2 L, ni (ni - 1) + L nm} x nbj (9) L, nm} X nbj = 2 x 2 + 4 x 3 = 16 paths i·l j=l j=l where ODd = 42 + 16 = 58 paths nm = the number of joint stations that the "double" line shares with the already counted "basic" OD,= OD - ODd = 105 - 58 = 47 paths line, nb = the numher of stations on the branches The .lQ elements expressing size and form of metro network are (single sections) of that line, and listed in Table 2.