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

Document Type

Journal Article

Publication Date


Subject Area

mode - bus, infrastructure - fleet management, operations - scheduling


Bus bunching, Multi-line transit operations, Headway control, Self-stabilization, Worst-case analysis


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.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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