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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. [ABSTRACT FROM AUTHOR]

Circuity, defined as the ratio of the shortest network distance to the Euclidean distance between one origin–destination (O-D) pair, can be adopted as a helpful evaluation method of indirect degrees of train paths. In this paper, the maximum circuity of the paths of operated trains is set to be the threshold value of the circuity of high-speed train paths. For the shortest paths of any node pairs, if their circuity is not higher than the threshold value, the paths can be regarded as the reasonable paths. With the consideration of a certain relative or absolute error, we cluster the reasonable paths on the basis of their inclusion relationship and the center path of each class represents a passenger transit corridor. We take the high-speed rail (HSR) network in China at the end of 2014 as an example, and obtain 51 passenger transit corridors, which are alternative sets of train paths. Furthermore, we analyze the circuity distribution of paths of all node pairs in the network. We find that the high circuity of train paths can be decreased with the construction of a high-speed railway line, which indicates that the structure of the HSR network in China tends to be more complete and the HSR network can make the Chinese railway network more efficient. [ABSTRACT FROM AUTHOR]