Robust bus scheduling considering transfer synchronizations

In this study, we model the bus scheduling problem considering transfer synchronizations. Our mathematical model accounts for the variability of the travel and dwell times of bus trips, the regularity of individual bus lines, and the regulatory constraints related to the schedule sliding prevention and the layover time limits. To perform a synchronization of multiple bus lines that is robust to travel time and dwell time variabilities, we tackle this problem using the minimax decision rule of 2-player games where one player selects the optimal dispatching times for some specific travel and dwell time noise, whereas the other player selects the worst-case travel and dwell time noise for a given dispatching time solution. In a validation of this approach in two bus lines in Stockholm using 1 month of actual vehicle location and passenger counting data, we demonstrate the potential improvement in terms of service regularity and increased synchronizations. Finally, we examine how the performance of bus schedules in common-case scenarios is affected when their robustness to extreme deviations is increased.