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arXiv · 1003.4012

Phase Synchronization in Railway Timetables

Christoph Fretter·Lachezar Krumov·Karsten Weihe·Matthias Müller-Hannemann·Marc-Thorsten Hütt
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Abstract

Timetable construction belongs to the most important optimization problems in public transport. Finding optimal or near-optimal timetables under the subsidiary conditions of minimizing travel times and other criteria is a targeted contribution to the functioning of public transport. In addition to efficiency (given, e.g., by minimal average travel times), a significant feature of a timetable is its robustness against delay propagation. Here we study the balance of efficiency and robustness in long-distance railway timetables (in particular the current long-distance railway timetable in Germany) from the perspective of synchronization, exploiting the fact that a major part of the trains run nearly periodically. We find that synchronization is highest at intermediate-sized stations. We argue that this synchronization perspective opens a new avenue towards an understanding of railway timetables by representing them as spatio-temporal phase patterns. Robustness and efficiency can then be viewed as properties of this phase pattern.

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Christoph Fretter, Lachezar Krumov, Karsten Weihe, Matthias Müller-Hannemann, Marc-Thorsten Hütt. 2010-03-21. Phase Synchronization in Railway Timetables. https://doi.org/10.1140/epjb/e2010-00234-y

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