Optimal design of fixed-route and demand-responsive transit with a dynamic stop strategy

To address the high detour costs associated with Demand-Responsive Transit (DRT) when feeding Fixed-Route Transit (FRT), this paper proposes an integration between FRT and DRT based on a dynamic stop strategy. This strategy allows passengers to, with an acceptable walking distance, connect their origins/destinations with dynamic stops. These stops have spacings that are randomly and uniformly distributed and are assigned to passengers upon their requests for DRT services. In this way, DRT does not need to pick up/drop off passengers at their origins/destinations, hence reducing the detour distance especially when the origins/destinations are far from FRT stops. Passengers may walk, take DRT directly, or combine the two to access FRT services. To deal with the modeling complexity that arises from the relationship between the three feeder modes, we divide the catchment zone of a FRT stop into different areas corresponding to different feeder modes, and evaluate transit agency and user costs based on the shapes of these areas using a parsimonious continuum approach. The optimal design for the integrated system is then formulated as a mixed-integer program that aims to minimize the total system cost, a combination of agency and user costs. Numerical experiments are conducted to compare the performance of the proposed system with two related transit systems in different scenarios. The results show that the proposed system could reduce agency costs by over 15% across different transit demand levels at the expense of minor changes in system costs, and demonstrate strong robustness to various potential changes in future.