Modelling reservation strategies for managing peak-hour stranding on an oversaturated metro line

Metro is the main travel model for urban commuters in many metropolises around the world. During peak hours, large numbers of passengers pour into metro stations for rail services, but some are unable to board the trains in time and left stranded on the platform or even queuing outside the stations. The trip reservation (TR) strategy, where passengers preplan their trips and reserve their entry time to the stations. This paper develops an entry reservation strategy (ERS) to optimize the commuter flow during peak hours, and construct a multi-objective passenger flow joint optimization model based on many-to-many passenger demand to minimize the total trip cost of passengers at reservation station and the number of stranded passengers at intermediate stations. The passenger flow optimization problem is formulated as a mixed-integer non-linear programming (MINLP) model. We design an iterative sequential search algorithm combined with the GUROBI solver to obtain the parameters of the optimal ERS and the passenger flow distribution in the metro system after disaggregated reformulation of the complex constraints of the model. We also demonstrate the accuracy and effectiveness of the proposed method with two experiments - an illustrative example and a large-scale case study of Beijing Metro. The results of Beijing Metro experiment show that the joint optimization model with entry reservation strategy (JO-ERS) reduces the number of stranded passengers by 88.46 % compared with the original passenger flow from the AFC.