An Integrated Model Predictive Control Method for the Rescheduling of Metro Traffic with Backup Trains

In large cities, metro lines are often saturated and impacted by sudden events to the point that some stations in the network become overcrowded and multiple trains are seriously delayed, causing the increase of passengers' waiting time. This disservice can be reduced by rescheduling the metro traffic and by adding backup trains in storage lines to be used when the service level largely decreases. In this paper, a novel control strategy, called Integrated Model Predictive Control, is proposed that combines both timetable rescheduling and backup trains allocation. In particular, a state-space model is adopted to describe the evolution of the train traffic dynamics and the model predictive control method is applied to obtain an optimal controller such that the rescheduled departure time and headway deviations from the nominal timetable are minimized. In the case where no feasible controller exists because of extensive delays, we propose an event-triggered process to automatically add backup trains into the operation plan such that the timetable can recover quickly. Finally, numerical examples are provided to demonstrate the effectiveness of the proposed control method.