A Symbolic Design Method for ETCS Hybrid Level 3 at Different Degrees of Accuracy

Authors Stefan Engels , Tom Peham , Robert Wille

Thumbnail PDF


  • Filesize: 1.16 MB
  • 17 pages

Document Identifiers

Author Details

Stefan Engels
  • Chair for Design Automation, Technical University of Munich, Germany
Tom Peham
  • Chair for Design Automation, Technical University of Munich, Germany
Robert Wille
  • Chair for Design Automation, Technical University of Munich, Germany
  • Software Competence Center Hagenberg GmbH (SCCH), Austria

Cite AsGet BibTex

Stefan Engels, Tom Peham, and Robert Wille. A Symbolic Design Method for ETCS Hybrid Level 3 at Different Degrees of Accuracy. In 23rd Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2023). Open Access Series in Informatics (OASIcs), Volume 115, pp. 6:1-6:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


The European Train Control System (Hybrid) Level 3 (ETCS Hybrid Level 3) allows for introducing Virtual Subsections (VSS) into existing railway infrastructures. These VSS work similarly to blocks in conventional block signaling but do not require installation or maintenance of trackside train detection. This added flexibility can be used to adapt a given railway network’s (virtual) layout to the changing demands of new schedules. Automated methods are needed to properly use this flexibility and design such layouts on demand and avoid time-intensive manual labor. Recently, approaches inspired by design automation of electronic hardware have been proposed to address this need. But those methods - which are particularly well suited for inherently discrete problems in electronic design automation - have struggled with modeling continuous properties like train positions, time, and acceleration. This work proposes a Mixed Integer Linear Programming (MILP) formulation that, for the first time, can accurately model design problems for ETCS Hybrid Level 3 by including essential, continuous constraints, e.g., for train dynamics or braking curves. The formulation is designed to be flexible and extendable, allowing the user to include/exclude certain constraints or simplify the model as needed. By this, the user can decide whether he/she wants to quickly generate a less accurate solution or a more accurate one at the expense of higher runtimes - basically allowing him/her to trade-off accuracy and efficiency. A case study showcases the potential of the proposed approach and sketches examples to analyze which trade-offs are worthwhile and which simplifications can be safely made. The resulting tool and the benchmarks considered in this work are publicly available at https://github.com/cda-tum/mtct (as part of the Munich Train Control Toolkit, MTCT).

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • ETCS
  • MILP
  • design automation
  • block signaling
  • virtual subsection


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


  1. Tobias Achterberg and Eli Towle. Non-convex quadratic optimization, 2020. URL: https://www.gurobi.com/events/non-convex-quadratic-optimization/.
  2. Maarten Bartholomeus, Laura Arenas, Roman Treydel, Francois Hausmann, Nobert Geduhn, and Antoine Bossy. ERTMS Hybrid Level 3. SIGNAL + DRAHT (110) 1+2/2018, pages 15-22, 2018. URL: https://www.eurailpress.de/fileadmin/user_upload/SD_1_2-2018_Bartholomaeus_ua.pdf.
  3. Ralf Borndörfer and Thomas Schlechte. Solving railway track allocation problems. In Operations Research Proceedings, pages 117-122. Springer Berlin Heidelberg, 2008. URL: https://doi.org/10.1007/978-3-540-77903-2_18.
  4. Malachy Carey and Sinead Carville. Scheduling and platforming trains at busy complex stations. Transportation Research Part A: Policy and Practice, 37(3):195-224, 2003. URL: https://doi.org/10.1016/S0965-8564(02)00012-5.
  5. C.S. Chang and D. Du. Further improvement of optimisation method for mass transit signalling block-layout design using differential evolution. IEE Proceedings - Electric Power Applications, 146(5):559, 1999. URL: https://doi.org/10.1049/ip-epa:19990223.
  6. Andrea D'Ariano, Dario Pacciarelli, and Marco Pranzo. A branch and bound algorithm for scheduling trains in a railway network. European Journal of Operational Research, 183(2):643-657, 2007. URL: https://doi.org/10.1016/j.ejor.2006.10.034.
  7. DB Netz AG. Infrastrukturregister, 2023. URL: https://geovdbn.deutschebahn.com/isr.
  8. DB Regio AG. Fahrpläne S-Bahn München, 2023. URL: https://www.s-bahn-muenchen.de/fahren/fahrplaene.
  9. Stefan Dillmann and Reiner Hähnle. Automated planning of ETCS tracks. In Reliability, Safety, and Security of Railway Systems. Modelling, Analysis, Verification, and Certification, pages 79-90. Springer International Publishing, 2019. URL: https://doi.org/10.1007/978-3-030-18744-6_5.
  10. EEIG ERTMS Users Group. ERTMS/ETCS hybrid train detection. Technical Report 16E042, ERTMS, 2022. Version 1E. URL: https://ertms.be/wp-content/uploads/2023/06/16E0421F_HTD.pdf.
  11. Stefan Engels, Tom Peham, Judith Przigoda, Nils Przigoda, and Robert Wille. Design tasks and their complexity for Hybrid Level 3 of the European Train Control System. CoRR, 2023. URL: https://doi.org/10.48550/arXiv.2308.02572.
  12. European Union Agency for Railways. Introduction to ETCS braking curves. Technical Report ERA_ERTMS_040026, European Union Agency for Railways, 2020. Version 1.5. URL: https://www.era.europa.eu/system/files/2022-11/Introduction%20to%20ETCS%20braking%20curves.pdf.
  13. O. Gemine, A. Hougardy, and E. Lepailleur. ERTMS unit: Assignment of values to ETCS variables. Technical Report ERA_ERTMS_040001, European Union Agency for Railways, 2023. Version 1.33. URL: https://www.era.europa.eu/system/files/2023-02/ETCS%20variables%20and%20values.pdf.
  14. D.C. Gill and C.J. Goodman. Computer-based optimisation techniques for mass transit railway signalling design. IEE Proceedings B Electric Power Applications, 139(3):261, 1992. URL: https://doi.org/10.1049/ip-b.1992.0031.
  15. Jan-Willem Goossens, Stan van Hoesel, and Leo Kroon. On solving multi-type railway line planning problems. European Journal of Operational Research, 168(2):403-424, 2006. URL: https://doi.org/10.1016/j.ejor.2004.04.036.
  16. Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual, 2023. URL: https://www.gurobi.com.
  17. Lylly Hernández and Sascha Hardel. Section breaks and level crossings limit capacity increases under ETCS Level 2. SIGNAL + DRAHT (115) 1+2 / 2023, pages 24-30, 2023. Google Scholar
  18. B.R. Ke and N. Chen. Signalling blocklayout and strategy of train operation for saving energy in mass rapid transit systems. IEE Proceedings - Electric Power Applications, 152(2):129, 2005. URL: https://doi.org/10.1049/ip-epa:20045188.
  19. 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.
  20. Thomas Künzel. Triebwagen für den zukünftigen Nah- und Regionalverkehr in Deutschland. PhD thesis, TU Berlin, 2019. URL: https://depositonce.tu-berlin.de/items/76de5c51-6cad-4250-abd5-df7b35643409.
  21. Richard M. Lusby, Jesper Larsen, Matthias Ehrgott, and David Ryan. Railway track allocation: models and methods. OR Spectrum, 33(4):843-883, December 2009. URL: https://doi.org/10.1007/s00291-009-0189-0.
  22. Richard M. Lusby, Jesper Larsen, Matthias Ehrgott, and David M. Ryan. A set packing inspired method for real-time junction train routing. Computers & Operations Research, 40(3):713-724, 2013. URL: https://doi.org/10.1016/j.cor.2011.12.004.
  23. Bjørnar Luteberget. Automated Reasoning for Planning Railway Infrastructure. PhD thesis, Univ. of Oslo, May 2019. URL: https://www.mn.uio.no/ifi/english/research/projects/railcons/documents/luteberget-thesis-b5-2019-09-17.pdf.
  24. Richard Oberdieck, Kostja Siefen, Jaromil Najman, and Ed Klotz. Tech talk - a practical tour through non-convex optimization, 2021. URL: https://www.gurobi.com/events/tech-talk-a-practical-tour-through-non-convex-optimization/.
  25. Jörn Pachl. Railway Signalling Principles: Edition 2.0. Universitätsbibliothek Braunschweig, 2021. URL: https://doi.org/10.24355/dbbs.084-202110181429-0.
  26. 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.
  27. Vahid Ranjbar, Nils O.E. Olsson, and Hans Sipilä. Impact of signalling system on capacity endash comparing legacy ATC, ETCS Level 2 and ETCS Hybrid Level 3 systems. Journal of Rail Transport Planning & Management, 23:100322, 2022. URL: https://doi.org/10.1016/j.jrtpm.2022.100322.
  28. 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.
  29. Lars Schnieder. Communications-Based Train Control (CBTC). Springer Berlin Heidelberg, March 2021. URL: https://doi.org/10.1007/978-3-662-62876-8.
  30. Lars Schnieder. European Train Control System (ETCS). Springer Berlin Heidelberg, 2021. URL: https://doi.org/10.1007/978-3-662-62878-2.
  31. Valeria Vignali, Federico Cuppi, Claudio Lantieri, Nicola Dimola, Tomaso Galasso, and Luca Rapagnà. A methodology for the design of sections block length on ETCS L2 railway networks. Journal of Rail Transport Planning & Management, 13:100160, 2020. URL: https://doi.org/10.1016/j.jrtpm.2019.100160.
  32. Robert Wille, Tom Peham, Judith Przigoda, and Nils Przigoda. Towards automatic design and verification for Level 3 of the European Train Control System. In 2021 Design, Automation & Test in Europe Conference & Exhibition (DATE). IEEE, 2021. URL: https://doi.org/10.23919/date51398.2021.9473935.
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