Optimization of unpaired timetable with express/local mode for the phenomenon of tidal passenger flow

For bi-directional subway lines, the number of passengers is not evenly distributed in the direction due to the tidal passenger flow phenomenon during peak hours, so the study of unpaired timetable has become a hot topic. The proposed optimization model optimizes the unpaired timetable with express/local (UTEL) mode by determining the number of trains running in each direction, departure headways and stopping schemes. In the proposed optimization model, a two-layer optimization structure is established, with the outer layer optimizing the train timetable including the rolling stock circulation constraints and the inner layer allocating passengers to each train, so as to reduce the total travel time cost of passengers and operational expenses. Using an actual subway line as an example, a cost-saving comparison between UTEL and train paired timetable with all-stop mode (PTAS) shows that UTEL reduces costs for both users and operators, and matches train capacity to passenger flow.