Real-time train timetabling with virtual coupling operations on a Y-type metro line

The spatiotemporal imbalance of passenger flows is a prominent characteristic of urban rail transit systems. To match the provided transportation capacity with passenger distribution, this study considers an integer linear programming model to optimize train operation on a Y-type line, including the train timetable, rolling stock circulation plan and virtual coupling/uncoupling strategy that enables trains to switch between different compositions or configurations during operations. To enhance solution efficiency, certain integer decision variables in the model are relaxed to be continuous, and it is proved that this does not affect the optimal value of the model. To account for the dynamic nature of passenger flows, a “prediction + optimization” method with the rolling optimization framework, which utilizes real-time predicted passenger flow data to enable train operations to be performed and adjusted in response, is proposed. Three variants of the proposed model are embedded to meet the real-time requirements of operations. Numerical experiments verify the effectiveness and applicability of our proposed approach, with real-world data from Shanghai Metro Line 5. The computational results demonstrate that our method performs well under operation scenarios with both normal and abnormal passenger flows. Compared to fixed train composition, virtual coupling can perform much better in both peak and off-peak periods.