Optimization of Bus Route Planning in Urban Commuter Networks

Bus routing is one of the most important elements of public transit system planning. This article presents a model for optimizing service headway and a bus route serving an area with a commuter (many-to-one) travel pattern. The bus route is optimized by minimizing the total system cost, including operator and user costs, while considering diagonal links in the study network. A method is developed for transforming this network into a pure grid, which enables construction of pure grid network models applicable to irregular grid networks. A case is presented to demonstrate the application of the model. Results show that the optimal bus route is sensitive to demand distribution over the service area. The developed model is particularly useful for planning a new bus service and evaluating an existing one in many cities embedded with general grid networks. Introduction Commuter bus routes are generally located on main thoroughfares of urban areas. However, considering realistic distributions of passenger travel demand over space and time, many route locations may not be cost-effective from either the operator or user standpoint. Therefore, relocating bus routes and redesigning headways may reduce operating costs as well as improve passenger accessibility. Both transit operators and passengers prefer short and fast routes to reduce the operating cost and travel time, respectively. However, passengers also prefer bus routes that can be easily accessed from their origins and destinations. To reduce Journal of Public Transportation, Vol. 6, No. 1, 2003 54 access impedance, tortuous routes are often constructed. This, in turn, is likely to increase both the in-vehicle portion of user travel time as well as the bus operating cost. Transit operators are well aware of this trade-off when planning a new bus route or extending an existing service. In the past 30 years, many researchers have analyzed the problems of optimal transit service design with many-to-one travel patterns by using analytical methods (Byrne and Vuchic 1971; Chang and Schonfeld 1991; Hurdle 1973; Spasovic and Schonfeld 1993; Spasovic et al.1994; Wirasinghe et al. 1977). They dealt with selecting zones, route/line spacings, headways, and route lengths designed to carry people between distributed origins and a single destination (e.g., central business district [CBD], transfer station, etc.). By assuming demand homogeneity of the service area, the researchers optimized the characteristics of bus systems consisting of a set of parallel routes feeding a major transfer station of a trunk line or a single terminal point, such as the CBD. A recent method for analyzing fixed-route bus systems is the out-of-direction (OOD) technique (Welch et al. 1991). This method improves the accessibility of a bus system by improving passenger accessibility along certain route segments. Chien and Schonfeld (1997) optimize a grid transit system in an urban area without oversimplifying the spatial and demand characteristics. They extended the model to jointly optimize the characteristics of a rail transit route and the associated feeder bus routes in an urban corridor (Chien and Schonfeld 1998). Chien and Yang (2000) developed an algorithm to search for the best bus route feeding a major intermodal station while considering the intersection delays and realistic street network. The model optimized the bus route location and operating headway by minimizing the sum of operator and user costs. It considered irregular and discrete demand realistically distributed over the service area. The route and headway were optimized analytically. In marked contrast to the above research, this article deals with the irregular grid street network, including diagonal streets and heterogeneous demand over the service area. To formulate bus routing problems, diagonal streets are transformed into horizontal and vertical links so the grid structure of the network could be preserved to facilitate the computational process. Actual lengths of diagonal links are taken into account when calculating the route length and travel times. The bus route, headway, and fleet size are optimized by minimizing the total cost (the sum