Designing transit-oriented multi-modal transportation systems considering travelers’ choices

One goal of future transit-oriented transportation systems is to promote door-to-door mobility for travelers by integrating different public transportation modes into a whole. We propose a mathematical design framework for such a transit-oriented multi-modal transportation system from a societal aspect considering three categories of public transportation modes, i.e., general on-demand modes, local on-demand modes, and fixed-schedule modes. A system-state equilibrium is brought up to describe travelers’ rational travel choices and their reverse effects on agency service levels using the continuous approximation method, and a centralized system designer then manages to achieve a system-beneficial outcome with the minimum cost. To solve the design problem, we prove that the transportation system reaches a unique equilibrium when decision variables are given. By this discovery, we construct a global search framework based on the DIRECT algorithm to solve the optimal design. In analyzing the problem property, we rigorously prove that in the designed systems, the bus service as a fixed-schedule mode is absent from the design scheme under the cases with sufficiently low demands, and the design problem thus reduces to a one-dimensional line search. The ride-hailing service as a general on-demand mode is similarly proved to be excluded when the demand is sufficiently high. In this context, the approximate design parameters of the bus service and the total system cost are developed analytically. The local on-demand mode, bike-sharing service, as an option of bus feeders, is proved to be efficient under a realistic setting. Extensive numerical examples provide evidence verifying the preceding analyses and indicating the behavior of travelers and agencies. Further sensitivity tests show that the subway is favorable for intensive demands and autonomous vehicles may promote the ride-hailing industry. For completeness, an immediate application of the proposed framework in generalized cases validates the model reliability