Probabilistic Simulation of a Railway Timetable

Authors Rebecca Haehn, Erika Ábrahám, Nils Nießen

Thumbnail PDF


  • Filesize: 0.62 MB
  • 14 pages

Document Identifiers

Author Details

Rebecca Haehn
  • RWTH Aachen University, LuFG THS, Germany
Erika Ábrahám
  • RWTH Aachen University, LuFG THS, Germany
Nils Nießen
  • RWTH Aachen University, VIA, Germany


We are gratefult to Deutsche Bahn for supporting us with data.

Cite AsGet BibTex

Rebecca Haehn, Erika Ábrahám, and Nils Nießen. Probabilistic Simulation of a Railway Timetable. In 20th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2020). Open Access Series in Informatics (OASIcs), Volume 85, pp. 16:1-16:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Railway systems are often highly utilized, which makes them vulnerable to delay propagation. In order to minimize delays timetables are desired to be robust, a property that is often estimated by simulating the respective timetable for different deterministic delay values. To achieve an accurate estimation under consideration of uncertain delays many simulation runs need to be executed. Most established simulation systems additionally use microscopic models of the railway systems, which further increases the simulations running times and makes them applicable rather for small areas of interest for complexity reasons. In this paper, we present a probabilistic, symbolic simulation algorithm for given timetables, this means we do not simulate individual executions, but all possible executions at once. We use a macroscopic model of the railway infrastructure as input. This way we consider the railway systems in less detail but are able to examine certain performance indicators for larger areas. For a given input model this simulation computes exact results. We implement the algorithm, examine its results, and discuss possible improvements of this approach.

Subject Classification

ACM Subject Classification
  • Computing methodologies → Model development and analysis
  • Railway
  • Modeling
  • Scheduling
  • Probabilistic systems
  • Optimization


  • Access Statistics
  • Total Accesses (updated on a weekly basis)
    PDF Downloads


  1. LUKS, 2020, (accessed July 1, 2020). URL:
  2. OnTime, 2020, (accessed July 1, 2020). URL:
  3. OpenTrack Railway Technology, 2020, (accessed July 1, 2020). URL:
  4. RailSys, 2020, (accessed July 1, 2020). URL:
  5. Emma Uhrdin Andersson. Assessment of robustness in railway traffic timetables, 2014. Google Scholar
  6. Thorsten Büker and Bernhard Seybold. Stochastic modelling of delay propagation in large networks. Journal of Rail Transport Planning and Management, 2(1):34-50, 2012. URL:
  7. Valentina Cacchiani and Paolo Toth. Nominal and robust train timetabling problems. European Journal of Operational Research, 219(3):727-737, 2012. Google Scholar
  8. Andrea D'Ariano. Improving real-time train dispatching: models, algorithms and applications, 2008. Google Scholar
  9. Andrea D’Ariano and Marco Pranzo. An advanced real-time train dispatching system for minimizing the propagation of delays in a dispatching area under severe disturbances. Networks and Spatial Economics, 9(1):63-84, 2009. Google Scholar
  10. Burkhard Franke, Bernhard Seybold, Thorsten Büker, Thomas Graffagnino, and Helga Labermeier. Ontime – network-wide analysis of timetable stability. In 5th International Seminar on Railway Operations Modelling and Analysis, May 2013. Google Scholar
  11. Sabine Radke (Deutsches Institut für Wirtschaftsforschung). Verkehr in Zahlen 2019/2020 (in German), 2019. Google Scholar
  12. Rob M. P. Goverde and Ingo A. Hansen. Performance indicators for railway timetables. In 2013 IEEE International Conference on Intelligent Rail Transportation Proceedings, pages 301-306, 2013. Google Scholar
  13. David Janecek and Frédéric Weymann. Luks - Analysis of lines and junctions. In Proceedings of the 12th World Conference on Transport Research (WCTR 2010), Lisbon, Portugal, 2010. Google Scholar
  14. Christian Liebchen, Michael Schachtebeck, Anita Schöbel, Sebastian Stiller, and André Prigge. Computing delay resistant railway timetables. Computers & Operations Research, 37(5):857-868, 2010. Disruption Management. URL:
  15. Andrew Nash and Daniel Huerlimann. Railroad simulation using OpenTrack. Computers in Railways IX, pages 45-54, 2004. URL:
  16. Alfons Radtke. Infrastructure modelling. Eurailpress, Hamburg, 2014. Google Scholar
  17. Alfons Radtke and Jan-Philipp Bendfeldt. Handling of railway operation problems with RailSys. In Proceedings of the 5th World Congress on Rail Research (WCRR 2001), Cologne, Germany, 2001. Google Scholar
  18. Richard L. Sauder and William M. Westerman. Computer aided train dispatching: decision support through optimization. Interfaces, 13(6):24-37, 1983. Google Scholar
  19. Walter Schneider, Nils Nießen, and Andreas Oetting. MOSES/WiZug: Strategic modelling and simulation tool for rail freight transportation. In Proceedings of the European Transport Conference, Straßbourg, 2003. Google Scholar
  20. Jianxin Yuan. Stochastic modelling of train delays and delay propagation in stations, volume 2006. Eburon Uitgeverij BV, 2006. Google Scholar
  21. Jianxin Yuan and Giorgio Medeossi. Statistical analysis of train delays and movements. Eurailpress, Hamburg, 2014. Google Scholar
Questions / Remarks / Feedback

Feedback for Dagstuhl Publishing

Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail