A novel model for transfer synchronization in transit networks and a Lagrangian-based heuristic solution method

To realize the benefits of network connectivity in transfer-based transit networks, it is critical to minimize transfer disutility for passengers by synchronizing timetables of intersecting routes. We propose a mixed-integer linear programming timetable synchronization model that incorporates new features, such as dwell time determination and vehicle capacity consideration, which have been largely overlooked in the literature at the scheduling stage. We introduce a new concept of pre-planned holding time, called transfer buffer time, to reduce the transfer waiting time, particularly for transfers to low-frequency routes, while taking into account the penalty of extra in-vehicle time for onboard passengers and the possible consequences on headway regularity of a route. We develop a Lagrangian relaxation-based heuristic to obtain high-quality solutions efficiently for large instances. Our experiments on instances with up to 12 transfer nodes in the City of Toronto, with a mixture of low- and high-frequency routes, illustrate the potential benefits of the proposed model over the state of the art. The results indicate that incorporating transfer buffer time, dwell time determination, and vehicle capacity consideration improves model outcomes considerably, also demonstrating the computational efficiency of our Lagrangian-based solution method.