Optimizing a desirable fare structure for a bus-subway corridor

This paper aims to optimize a desirable fare structure for the public transit service along a bus-subway corridor with the consideration of those factors related to equity in trip, including travel distance and comfort level. The travel distance factor is represented by the distance-based fare strategy, which is an existing differential strategy. The comfort level one is considered in the area-based fare strategy which is a new differential strategy defined in this paper. Both factors are referred to by the combined fare strategy which is composed of distance-based and area-based fare strategies. The flat fare strategy is applied to determine a reference level of social welfare and obtain the general passenger flow along transit lines, which is used to divide areas or zones along the corridor. This problem is formulated as a bi-level program, of which the upper level maximizes the social welfare and the lower level capturing traveler choice behavior is a variable-demand stochastic user equilibrium assignment model. A genetic algorithm is applied to solve the bi-level program while the method of successive averages is adopted to solve the lower-level model. A series of numerical experiments are carried out to illustrate the performance of the models and solution methods. Numerical results indicate that all three differential fare strategies play a better role in enhancing the social welfare than the flat fare strategy and that the fare structure under the combined fare strategy generates the highest social welfare and the largest resulting passenger demand, which implies that the more equity factors a differential fare strategy involves the more desirable fare structure the strategy has.