Optimal transit service atop ring-radial and grid street networks : a continuum approximation design method and comparisons

Abstract

Two continuum approximation (CA) optimization models are formulated to design city-wide transit systems at minimum cost. Transit routes are assumed to lie atop a city's street network. Model 1 assumes that the city streets are laid out in ring-radial fashion. Model 2 assumes that the city streets form a grid. Both models can furnish hybrid designs, which exhibit intersecting routes in a city's central (downtown) district and only radial branching routes in the periphery. Model 1 allows the service frequency and the route spacing at a location to vary arbitrarily with the location's distance from the center. Model 2 also allows such variation but in the periphery only. The paper shows how to solve these CA optimization problems numerically, and how the numerical results can be used to design actual systems. A wide range of scenarios is analyzed in this way. It is found among other things that in all cases and for both models: (i) the optimal headways and spacings in the periphery increase with the distance from the center; and (ii) at the boundary between the central district and the periphery both, the optimal service frequency and line spacing for radial lines decrease abruptly in the outbound direction. On the other hand Model 1 is distinguished from Model 2 in that the former produces in all cases: (i) a much smaller central district, and (ii) a high frequency circular line on the outer edge of the central district. Parametric tests with all the scenarios further show that Model 1 is consistently more favorable to transit than Model 2. Cost differences between the two designs are typically between 9% and 13%, but can top 21.5%. This is attributed to the manner in which ring-radial networks naturally concentrate passenger's shortest paths, and to the economies of demand concentration that transit exhibits. Thus, it appears that ring-radial street networks are better for transit than grids. In order to illustrate the robustness of the CA design procedure to irregularities in real street networks, the results for all the test problems were then used to design and evaluate transit systems on networks of the "wrong" type - grid networks were outfilled with transit systems designed with Model 1 and ring-radial networks designed with Model 2. Cost increased on average by a little 2.7%. The magnitude of these deviations suggests that the proposed CA procedures can be used to design transit systems over real street networks when they are not too different from the ideal and that the resulting costs should usually be very close to those predicted.