Eur. Phys. J. B 77, 281-289 (2010)
https://doi.org/10.1140/epjb/e2010-00234-y

Phase synchronization in railway timetables

¹ Institut für Informatik, Martin-Luther-Universität Halle-Wittenberg, 06120 Halle, Germany
² Fachgebiet Algorithmik, Technische Universität Darmstadt, 64289 Darmstadt, Germany
³ School of Engineering and Science, Jacobs University, 28759 Bremen, Germany

Corresponding author: ^a fretter@informatik.uni-halle.de

Received: 16 March 2010
Revised: 27 May 2010
Published online: 11 August 2010

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.