Transit timetable synchronization for transfer time minimization

Abstract

This paper aims to synchronize timetables in a transit network so as to minimize the total passenger transfer waiting time. Assuming a fixed headway for each line, we first formulate the problem as an optimization problem with congruence constraints. We show that the problem is NP-hard, and investigate several special cases of the problem that are solvable in polynomial time. Furthermore, we show that the local search for the general problem is equivalent to the well-studied maximum directed cut problem. As such, we use an approximation algorithm for the maximum directed cut problem to solve the timetable synchronization problem. We assess the quality of the algorithm on a real-world case study, and show that our algorithm significantly outperforms the state-of-the-art in the literature. Lastly, we relax the fixed headway assumption, and propose an efficient recursive quasi-linear time algorithm to minimize the total transfer waiting time in this general setting.