Joint Optimal Train Rescheduling and Passenger Flow Control for Speed Limit and High-Demand Scenarios of Urban Rail Transits

In the operation of urban rail transits, train delays occur frequently, and emergency management is one of the key factors to ensure the service quality. For speed limit scenarios with high demand, this paper takes the train running in the restricted manual (RM) mode in the speed limit zone as an example and discusses a coping method by jointing train rescheduling and passenger flow control. With the goal of maximizing the number of passengers served and minimizing total train delay, a nonlinear optimization model is constructed by taking the train operation-related requirements and passenger flow control-related indicators as constraints, and the model is reformulated to a mixed-integer programming (MIP) model with quadratic constraints, which can be solved by the Gurobi solver. In order to obtain effective solutions faster, a two-stage approach is discussed, which first obtains a rescheduling timetable and then dynamically adjusts the requirement of boarding equalization to obtain the passenger flow control scheme. The validity of the model and the solution approach are discussed with the help of numerical experiments. The results suggest that the model and solution approach are feasible. When the number of trains is fixed, the reasonable implementation of passenger flow control will help to increase the number of passengers served, and the pursuit of a higher equalization of boarding is not conducive to the number of passengers served and the full utilization of transport capacity. The two-stage approach has certain advantages over the direct computing method. The methods in this paper have a guiding value for emergency decision-making in similar delay scenarios.