Robust Network-Wide Bus Scheduling with Transfer Synchronizations

Travel time and demand disturbances lead to unreliable bus operations and missed passenger transfers. This study formulates the multi-line synchronization problem as a robust min(i)max problem that considers the fluctuations of the travel and dwell times of bus trips. Given the infeasibility of the multi-line synchronization problem in extreme cases of travel/dwell time disturbances, we introduce a flexible problem formulation that incorporates the constraint violations into the objective function. To produce a robust schedule, the dispatching times of trips are our design variables and the travel and dwell time fluctuations are the environmental variables which have an adversarial role in our minimax problem. We validate our approach in the bus network of The Hague using 1 month of actual vehicle location and passenger counting data. There, we demonstrate the potential improvement in terms of service regularity and increased synchronizations in common case and extreme case conditions.