Document Open Access Logo

Time-Aware A* for Optimal Train Routing on Moving Block Systems

Authors Stefan Engels , Robert Wille

PDF

File

Thumbnail PDF
PDF
OASIcs.ATMOS.2026.3.pdf
  • Filesize: 3.22 MB
  • 19 pages

Document Identifiers

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
Keywords
  • ETCS
  • European Train Control System
  • Train Routing
  • Moving Block
  • A*
  • Search Space Reduction
  • Munich Train Control Toolkit

Metrics

Abstract

Railway networks are operating at their capacity limits. Modern control systems allow for shorter train-following times on existing infrastructure, resulting in faster travel times and higher capacity. As new degrees of freedom emerge, developing effective and flexible algorithms becomes essential to incorporate these advancements into the planning process. Previously, a flexible method for generating provably optimal timetables using A* search has been proposed. However, in practice, the algorithm spends significant time exploring states that yield no new information. This work addresses this issue and shows that transforming the state space into a (directed) tree drastically reduces runtime and enhances scalability, particularly with respect to the number of trains. The implementation is available open-source as part of the Munich Train Control Toolkit on GitHub at https://github.com/cda-tum/mtct.

Cite As Get BibTex

Stefan Engels and Robert Wille. Time-Aware A* for Optimal Train Routing on Moving Block Systems. In 26th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2026). Open Access Series in Informatics (OASIcs), Volume 147, pp. 3:1-3:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/OASIcs.ATMOS.2026.3

Author Details

Stefan Engels
  • Chair for Design Automation, Technical University of Munich, Germany
Robert Wille
  • Chair for Design Automation, Technical University of Munich, Germany

Supplementary Materials

References

  1. Ralf Borndörfer, Torsten Klug, Leonardo Lamorgese, Carlo Mannino, Markus Reuther, and Thomas Schlechte, editors. Handbook of Optimization in the Railway Industry. Springer International Publishing, 2018. URL: https://doi.org/10.1007/978-3-319-72153-8.
  2. Stefan Engels and Robert Wille. Munich Train Control Toolkit. Software, (visited on 2026-09-22). URL: https://github.com/cda-tum/mtct
    Software Heritage Logo archived version
    full metadata available at: https://doi.org/10.4230/artifacts.28078
  3. Stefan Engels and Robert Wille. Comparing lazy constraint selection strategies in train routing with moving block control. In Proceedings of the 19th Conference on Computer Science and Intelligence Systems (FedCSIS), volume 39, pages 585-590. Polish Information Processing Society, 2024. URL: https://doi.org/10.15439/2024f3041.
  4. Stefan Engels and Robert Wille. Using A* for optimal train routing on moving block systems. In 25th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, ATMOS 2025, Warsaw, Poland, September 18-19, 2025, volume 137, pages 14:1-14:18. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2025. URL: https://doi.org/10.4230/OASIcs.ATMOS.2025.14.
  5. Peter E. Hart, Nils J. Nilsson, and Bertram Raphael. A formal basis for the heuristic determination of minimum cost paths. IEEE Trans. Systems Science and Cybernetics, 4(2):100-107, 1968. URL: https://doi.org/10.1109/TSSC.1968.300136.
  6. Simon Hofmann, Marcel Walter, and Robert Wille. A* is born: Efficient and scalable physical design for field-coupled nanocomputing. In 2024 IEEE 24th International Conference on Nanotechnology (NANO), pages 80-85. IEEE, 2024. URL: https://doi.org/10.1109/nano61778.2024.10628808.
  7. Torsten Klug, Markus Reuther, and Thomas Schlechte. Does laziness pay off? - a lazy-constraint approach to timetabling. In Mattia D'Emidio and Niels Lindner, editors, 22nd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2022), volume 106. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2022. URL: https://doi.org/10.4230/OASIcs.ATMOS.2022.11.
  8. Jörn Pachl. Railway Signalling Principles: Edition 2.0. Universitätsbibliothek Braunschweig, 2021. URL: https://doi.org/10.24355/dbbs.084-202110181429-0.
  9. Tom Peham, Judith Przigoda, Nils Przigoda, and Robert Wille. Optimal railway routing using virtual subsections. In Reliability, Safety, and Security of Railway Systems. Modelling, Analysis, Verification, and Certification, pages 63-79. Springer International Publishing, 2022. URL: https://doi.org/10.1007/978-3-031-05814-1_5.
  10. Ira Pohl. First results on the effect of error in heuristic search. In Bernard Meltzer and Donald Michie, editors, Machine Intelligence 5, pages 219-236. Edinburgh University Press, Edinburgh, 1970. Google Scholar
  11. Thomas Schlechte, Ralf Borndörfer, Jonas Denißen, Simon Heller, Torsten Klug, Michael Küpper, Niels Lindner, Markus Reuther, Andreas Söhlke, and William Steadman. Timetable optimization for a moving block system. Journal of Rail Transport Planning & Management, 22:100315, 2022. URL: https://doi.org/10.1016/j.jrtpm.2022.100315.
  12. Lars Schnieder. Communications-Based Train Control (CBTC). Springer Berlin Heidelberg, March 2021. URL: https://doi.org/10.1007/978-3-662-62876-8.
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact