A New Method for Inserting Train Paths into a Timetable

TL;DR

A fast and scalable path-insertion algorithm based on dynamic programming that is able to output multiple suitable paths for a freight train within 0.3 seconds after preprocessing is proposed.

Abstract

A seemingly simple, yet widely applicable subroutine in automated train scheduling is the insertion of a new train path to a timetable in a railway network. We believe it to be the first step towards a new train-rerouting framework in case of large disturbances or maintenance works. Other applications include handling ad-hoc requests and modifying train paths upon request from railway undertakings. We propose a fast and scalable path-insertion algorithm based on dynamic programming that is able to output multiple suitable paths. Our algorithm uses macroscopic data and can run on railway networks with any number of tracks. We apply the algorithm on the line from Göteborg Sävenäs to the Norwegian border at Kornsjö. For a time window of seven hours, we obtain eight suitable paths for a freight train within 0.3 seconds after preprocessing.

Figures (4)

• Figure 1: A graph class where there exists an arc ordering that is consistent with all $u$-$v$ paths. Such an ordering can, for example, be obtained by iteratively adding all arcs to the next layer, all downward arcs in its subsequent layer and all upward arcs in that layer.
• Figure 2: By adding one arc to a graph from the graph class in Figure \ref{['fig:nice-consistency']}, no arc ordering is consistent with all $u$-$v$ paths. Consider $u$-$v$ path and its mirrored counterpart in \ref{['fig:init-b']}. The displayed path requires arc (2) before arc (1) in the ordering, while the mirrored path requires (1) before (2).
• Figure 3: The eight candidate paths for a freight train from Göteborg Sävenäs to Kornsjö. Locations where trains can overtake or meet each other are indicated with horizontal, grey lines. One existing path uses side tracks for which the opposing tracks have to be crossed. We do not consider this behavior, as crossing opposing tracks consumes relatively much capacity, but it can easily be included in the algorithm.
• Figure 4: Evaluation of the path insertion algorithm.