A Bi-Level Approach for the Metro Train Scheduling Problem Considering Passenger Behaviors

In urban rail systems, the performance of a train schedule is directly related to the attractiveness to passengers, since the passengers may choose other transport modes in case of station crowdedness. In this paper, we are devoted to the problem of train scheduling in urban rail systems with consideration of passenger behaviors. Specifically, we construct a bi-level model for this problem, where the upper level optimizes the train schedule as well as train stop-skipping strategies, while the lower level models the choice of passengers given the train schedule from the upper level. An iterative framework is proposed to solve the bi-level model. We carry out the simulation experiment using the actual data of Beijing Metro Line 1. The simulation results show that our bi-level approach can generate a more attractive train schedule that increases the number of traveling passengers by 17.39 %.