An exact method for real-time rescheduling after disturbances in metro lines

This study proposes an exact model for timetable recovery after disturbances. Our model is applicable to high frequency services that operate under frequencies of at least 5 trips per hour. The objective of our model is the minimization of the deviation between the actual headways and their planned (target) values - a typical objective in high frequency services that indicates the service regularity. In the formulation of the timetable recovery model, we focus on metro lines with stable dwell times at stations that are not sensitive to changes in passenger demand. The resulting model is nonlinear and non-smooth; thus, it cannot be solved to optimality. To rectify this, we propose a model reformulation using slack variables. The reformulated program is equivalent to the original one and can be solved to global optimality in real time with exact optimization methods for quadratic programming. With our model, we investigate how many upstream trips should be rescheduled to respond to a service disturbance using real data from the red metro line inWashington D.C. Our experiments demonstrate an improvement potential of the service regularity by up to 30% if we reschedule the five upstream trips of a disrupted train.