A self-organizing policy for vehicle dispatching in public transit systems with multiple lines

In this paper, we propose and analyze an online, decentralized policy for dispatching vehicles in a multi-line public transit system. In the policy, vehicles arriving at a terminal station are assigned to the lines starting at the station in a round-robin fashion. Departure times are selected to minimize deviations from a certain target headway. We prove that this policy is self-organizing: given that there is a sufficient number of available vehicles, a timetable spontaneously emerges that meets the target headway of every line. Moreover, in case one of the vehicles breaks down, the remaining vehicles automatically redistribute over the network to re-establish such a timetable. We present both theoretical and numerical results on the time until a stable state is reached and on how quickly the system recovers after the breakdown of a vehicle. Experiments on three real-world transit systems show that our policy performs well, even if not all assumptions required for the theoretical analysis are met: if there are enough vehicles, the realized headways are typically close to the target headways. These promising results suggest that our self-organizing policy could be useful in situations where centralized dispatching is impractical or simply impossible due to an abundance of disruptions or the absence of information systems.