40 TRANSPORTATION RESEARCH RECORD 1120 A Methodology for Feeder-Bus Network Design GEoK KooN KuAH AND JossEF PERL The U.S. transit Industry faces financial difficulties. Among the transit services; and (h) development of better-integrated inter­ strategies suggested for Improving transit financial conditions, modal systems. the development of better-Integrated intermodal systems has Each of these strategies has its shortcomings. New funding the advantage of potentially achieving both cost reduction and schemes may be infeasible under the current political climate, Improved service. A network optimization methodology for the because they would require governments to increase taxes for design of an Integrated feeder-bus-rail rapid transit system is presented. The Feeder-Bus Network Design Problem (FBNDP) mass transit. New fare structures based on distance or time, or is defined as that of designing a set of feeder-bus routes and both, may increase revenue (depending on demand elasticities) determining the frequency on each route so as to minimize with a loss of patronage to the automobile mode. Such a shift operator and user costs. The FBNDP is first considered under would increase the need for investments in highway facilities many-to-one demand and Its formulation is discussed as a and would have negative environmental impacts. Service im­ mathematical programming problem. Then the generalization provements would result in higher transit operating costs, of the formulation to the many-to-many demand pattern is reviewed. The FBNDP Is a larger and complex routing-type which most likely would not be fully compensated for by problem that can be solved only heuristically. A heuristic increased revenues. The logic behind the strategy of shedding method that generalizes the savings approach to consider oper­ the peak is that a substantial proportion of transit investment is ating frequency is presented. The analysis presented Illustrates needed only for peak-period service. If private operators could the capabilities of the proposed model as a strategic planning share the burden of these services, it would reduce the capital tool for feeder-bus network design. It indicates that changes requirements of transit agencies. The success of the strategy of that increase the relative weight of operator cost often result in shedding the peak as well as that of privatization depends on feeder-bus networks with less circuitous routes operated at lower frequencies, whereas changes that increase the relative the willingness of the private sector to enter the transit industry, weight of user cost result in feeder routes operated at higher which, so far, has been limited. frequencies. The solutions provided by the proposed model The strategy of reducing (or eliminating) services to low­ have been tested and found superior to manually designed density areas may cause some captive riders to lose their networks, particularly under variable demand. mobility. Public transit operators may be reluctant to consider this strategy (4). The employment of more cost-effective trans­ portation technologies, such as vanpools, carpools, paratransit, The U.S. transit industry faces financial difficulties (1). Rising and taxi, has in some cases reduced the cost of transit services. costs and shrinking resources are the main causes for these However, these technologies are suitable primarily for low­ difficult financial conditions. From 1960 to 1983, the annual density areas and are usable only as components of an inte­ urban transit operating costs rose by more than $6. 7 billion. grated intermodal transit system. Only a small declining fraction of these operating expenditures The development of beuer-integrated intermodai transit sys­ were covered by farebox revenues (2, 3). In recent years, the tems can achieve both reduction in cost and improvement in uncertain financial conditions of the transit industry have been service quality. Better integration can reduce transit cost by made more acute by the reductions in federal funding for mass eliminating duplications and employing the most cost-effective transit. Since FY 1981, total federal funding available for mass mode in each segment of the system. An improvement in transit has declined by 28 percent (2). In view of declining service quality would result from better coverage and reduced federal assistance, transit agencies can expect to face growing access cost, fewer transfers, and shorter travel times. fu turn, pressure to reduce deficits. improved service would increase revenues to provide further Several strategies have been suggested for improving the deficit reduction. One type of integration with specific addi­ financial conditions of transit agencies: (a) new funding tional advantages involves the employment of bus transporta­ schemes to raise subsidies from local or state governments, or tion as access mode to a rail rapid transit system. First, a well­ both: (b) new fare structures to increase revenues; (c) improve­ iniegraied feeder-bus-raii rapid iransii sysiem retlu1,;es parking ments in service quality to attract ridership; (d) reduction in the requirements at the rail stations, thereby reducing the rail commitment to peak-period services ("shedding the peak"); system's capital cost. Second, a well-integrated feeder-bus-rail (e) reduction or elimination of services to low-density areas; (f) system may attract automobile trips (primarily work trips), use of more cost-effective technologies; (g) privatization of thereby increasing the economic viability of the rail system. The potential for improving the financial condition of transit G. K. Kuah, Gorove/Slade Associates, Inc., 1140 Connecticut Avenue, N.W., Suite 1200, Washington, D.C. 20036. J. Perl, Department of by designing an integrated feeder-bus-rail rapid transit system Civil Engineering, University of Maryland, College Park, Md. 20742. has heen recognized for some time (5-8). The integration of Kuah and Perl 41 feeder bus and rail rapid transit has been suggested as one of Two different demand patterns are considered-many-to­ the most promising future directions for public transit in large one and many-to-many. Many-to-one (M-to-1) refers to a de­ U.S. cities. In the last 15 years, several new rail rapid transit mand pattern with multiple origins and a single destination. systems have been constructed in large U.S. cities (San Fran­ Peak-period work trips to and from the central business district cisco; Atlanta; Washington, D.C.; Buffalo; Miami). The bus (CBD) may exhibit this pattern. Many-to-many (M-to-M) de­ and rail rapid transit systems in most of these cities are not well mand refers to a pattern with multiple origins and destinations. integrated (9). A common practice in designing feeder-bus Clearly, nonwork trips would likely follow this pattern. networks has been to turn the buses back at the nearest rail stations. The duplication of bus service along rail lines is also a common phenomenon (9). M-to-1 FBNDP There is currently no methodology for designing an inte­ grated feeder-bus-rail transit network. Most of the existing In the development of a network optimization model for the work on transit network design has focused on single-mode M-to-1 FBNDP, the following assumptions are made: networks (10-12). Often the focus has been on individual components of the network-design problem such as route struc­ 1. Each bus stop is served by one feeder-bus route. ture (13-15), service frequency (16, 17), and station spacing 2. Each bus route is linked to exactly one rail station. (18, 19). Results are presented of a recent study in which a 3. Buses have standard capacity and operating speed. network optimization methodology was developed for design­ ing an integrated feeder-bus-rail transit system. The proposed The first assumption may appear restrictive. However, It 1s methodology focuses on the network design elements of the valid for a system serving M-to-1 demand. When all the pas­ integration problem while including related operational ele­ sengers have a common destination, it is unnecessary to have ments such as service frequency. multiple bus routes serving the same bus stop. This assumption is relaxed in the case of the M-to-M demand pattern. The second assumption implies that buses are not allowed to travel THE FEEDER-BUS NETWORK DESIGN PROBLEM along rail lines. This assumption is consistent with one of the basic purposes of integration discussed earlier-the elimination Integrated feeder-bus-rail transit systems have a variety of of duplicate services. The third assumption is consistent with design components, which may include the network structure the common practice of operating fixed-route transit service of the rail and bus systems and the levels of service on each with the same type of vehicle. It is also a widely accepted component of the system. However, the basic decisions regard­ assumption in mathematical models for routing-type problems, ing the structure of the rail network, such as the locations of rail which significantly reduces the complexity of the models. lines and rail stations, are based on projected land use and are Figure 1 presents a feeder-bus-rail transit system with five not greatly affected by decisions regarding the feeder-bus sys­ rail lines serving a single destination. Also shown are the tem. The integration problem can therefore be viewed as one of feeder-bus routes for two of the rail lines. The feeder-bus-rail designing a feeder-bus system that can access an existing rail system shown in Figure 1 can be represented as a spanning-tree network, which is defined as the Feeder-Bus Network Design network (Figure 2) in which the destination is the root, the rail Problem (FBNDP). Specifically, the FBNDP is the problem of stations are first-level nodes, and the bus stops are higher-level designing a set of feeder-bus routes and determining the service nodes. Figure 2 constitutes a conceptual representation of an frequency on each route so as to minimize the sum of operator integrated feeder-bus-rail system, to be used in the formulation and user costs.