Timetable synchronization of the first train with multiple departure stations in urban rail transit networks

With the development of urban rail transit systems, the operation and management of the system faces various problems, among which the unreasonably long waiting time at transfer stations during the first train period is a major challenge for metro companies. To address this problem, some cities (e.g. Guangzhou, Hefei) are operating inter-regional trains to reduce the waiting time of passengers. With this motivation, we study the first train timetable synchronization problem with multiple departure stations. The problem is first formulated as a mixed integer nonlinear programming (MINLP) model. By using auxiliary intermediate variables, the nonlinear model is reformulated as a mixed integer linear programming (MILP) model, which can be solved directly by the commercial solver COPT. A real-world example of the Hefei urban rail transit network is applied to test the effectiveness of the proposed model. By adjusting the first ordinary train start service times and operating 12 additional inter-regional trains on 2 bidirectional lines, the total transfer waiting time and the number of long waiting time directions decreased by 39.09% and 56.25%, respectively.