Synthesis of Railway Signaling Layout from Local Capacity Specifications

  • Bjørnar Luteberget
  • Christian Johansen
  • Martin SteffenEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11800)


We present an optimization-based synthesis method for laying out railway signaling components on a given track infrastructure to fulfill capacity specifications. The specifications and the optimization method are designed to be suitable for the scope of signaling construction projects and their associated interlocking systems, but can be adapted to related problems in, e.g., highway, tram, or airport runway designs. The main synthesis algorithm starts from an initial heuristic over-approximation of required signaling components and iterates towards better designs using two main optimization techniques: (1) global simultaneous planning of all operational scenarios using incremental SAT-based optimization to eliminate redundant signaling components, and (2) a derivative-free numerical optimization method using as cost function timing results given by a discrete event simulation engine, applied on all the plans from (1).

Synthesizing all of the signaling layout might not always be appropriate in practice, and partial synthesis from an already valid design is a more practical alternative. In consequence, we focus also on the usefulness of the individual optimization steps: SAT-based planning is used to suggest removal of redundant signaling components, whereas numerical optimization of timing results is used to suggest moving signaling components around on the layout, or adding new components. Such changes are suggested to railway engineers using an interactive tool where they can investigate the consequences of applying the various optimizations.


Railway signaling Capacity On-the-fly synthesis Incremental SAT Interactive Derivative-free numerical optimization Discrete event simulation 


  1. 1.
    Abril, M., Barber, F., Ingolotti, L., Salido, M., Tormos, P., Lova, A.: An assessment of railway capacity. Transp. Res. Part E: Logistics Transp. Rev. 44(5), 774–806 (2008).
  2. 2.
    Basile, D., et al.: On the industrial uptake of formal methods in the railway domain. In: Furia, C.A., Winter, K. (eds.) IFM 2018. LNCS, vol. 11023, pp. 20–29. Springer, Cham (2018). Scholar
  3. 3.
    Biere, A., Cimatti, A., Clarke, E.M., Strichman, O., Zhu, Y.: Bounded model checking. Adv. Comput. 58(11), 117–148 (2003). Scholar
  4. 4.
    Biere, A., Heule, M., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press (2009)Google Scholar
  5. 5.
    Björk, M.: Successful SAT encoding techniques. J. Sat. Boolean Model. Comput. 7(4), 189–201 (2011).
  6. 6.
    Borälv, A., Stålmarck, G.: Formal verification in railways. In: Hinchey, M.G., Bowen, J.P. (eds.) Industrial-Strength Formal Methods in Practice, pp. 329–350. Springer (1999),
  7. 7.
    Boulanger, J.L.: CENELEC 50128 and IEC 62279 Standards. Wiley-ISTE, March 2015Google Scholar
  8. 8.
    Brent, R.P.: Algorithms for Minimization Without Derivatives. Dover Publications, Mineola (2002)zbMATHGoogle Scholar
  9. 9.
    Büker, T., Seybold, B.: Stochastic modelling of delay propagation in large networks. J. Rail Transp. Plan. Manag. 2(1–2), 34–50 (2012). Scholar
  10. 10.
    Cimatti, A., et al.: Formal verification and validation of ERTMS industrial railway train spacing system. In: Madhusudan, P., Seshia, S.A. (eds.) CAV 2012. LNCS, vol. 7358, pp. 378–393. Springer, Heidelberg (2012). Scholar
  11. 11.
    Dillmann, S., Hähnle, R.: Automated planning of ETCS tracks. In: Collart-Dutilleul, S., Lecomte, T., Romanovsky, A. (eds.) RSSRail 2019. LNCS, vol. 11495, pp. 79–90. Springer, Cham (2019). Scholar
  12. 12.
    Fantechi, A.: Twenty-five years of formal methods and railways: what next? In: Counsell, S., Núñez, M. (eds.) SEFM 2013. LNCS, vol. 8368, pp. 167–183. Springer, Cham (2014). Scholar
  13. 13.
    Hansen, I.A., Pachl, J.: Railway Timetabling and Operations. Eurailpress (2014)Google Scholar
  14. 14.
    Harris, T., Ross, F.S.: Fundamentals of a method for evaluating rail net capacities. Technical report, RM-1573, Rand Corporation (1955)Google Scholar
  15. 15.
    Hartonas-Garmhausen, V., Campos, S.V.A., Cimatti, A., Clarke, E.M., Giunchiglia, F.: Verification of a safety-critical railway interlocking system with real-time constraints. Sci. Comput. Program. 36(1), 53–64 (2000).
  16. 16.
    Haxthausen, A.E., Peleska, J., Kinder, S.: A formal approach for the construction and verification of railway control systems. Formal Aspects Comput. 23(2), 191–219 (2011). Scholar
  17. 17.
    Hürlimann, D.: Objektorientierte Modellierung von Infrastrukturelementen und Betriebsvorgängen im Eisenbahnwesen. Ph.D. thesis, ETH Zurich (2002).
  18. 18.
    Kamburjan, E., Hähnle, R., Schön, S.: Formal modeling and analysis of railway operations with active objects. Sci. Comput. Program. 166, 167–193 (2018).
  19. 19.
    Landex, A.: Methods to estimate railway capacity and passenger delays. Ph.D. thesis, Technical University of Denmark (DTU) (2008).
  20. 20.
    Luteberget, B.: Automated Reasoning for Planning Railway Infrastructure. Ph.D. thesis, Faculty of Mathematics and Natural Sciences, University of Oslo (2019)Google Scholar
  21. 21.
    Luteberget, B., Claessen, K., Johansen, C.: Design-time railway capacity verification using SAT modulo discrete event simulation. In: Bjørner, N., Gurfinkel, A. (eds.) Formal Methods in Computer Aided Design (FMCAD), pp. 1–9. IEEE (2018).
  22. 22.
    Luteberget, B., Johansen, C.: Efficient verification of railway infrastructure designs against standard regulations. Formal Methods Syst. Des. 52(1), 1–32 (2018). Scholar
  23. 23.
    Luteberget, B., Johansen, C., Feyling, C., Steffen, M.: Rule-based incremental verification tools applied to railway designs and regulations. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds.) FM 2016. LNCS, vol. 9995, pp. 772–778. Springer, Cham (2016). Scholar
  24. 24.
    Luteberget, B., Johansen, C., Steffen, M.: Rule-based consistency checking of railway infrastructure designs. In: Ábrahám, E., Huisman, M. (eds.) IFM 2016. LNCS, vol. 9681, pp. 491–507. Springer, Cham (2016). Scholar
  25. 25.
    Mao, B., Liu, J., Ding, Y., Liu, H., Ho, T.K.: Signalling layout for fixed-block railway lines with real-coded genetic algorithms. Hong Kong Inst. Eng. Trans. 13(1), 35–40 (2006). Scholar
  26. 26.
    Nocedal, J., Wright, S.J.: Numerical Optimization, 2nd edn. Springer, Heidelberg (2006). Scholar
  27. 27.
    Pachl, J.: Railway Operation and Control. VTD Rail Publishing (2015)Google Scholar
  28. 28.
    Robinson, S.: Simulation: The Practice of Model Development and Use. John Wiley & Sons Inc., New York (2004)Google Scholar
  29. 29.
    Vu, L.H., Haxthausen, A.E., Peleska, J.: A domain-specific language for railway interlocking systems. In: Schnieder, E., Tarnai, G. (eds.) Proceedings of the 10th Symposium on Formal Methods for Automation and Safety in Railway and Automotive Systems, (FORMS/FORMAT). pp. 200–209. TU Braunschweig (2014)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Bjørnar Luteberget
    • 1
  • Christian Johansen
    • 2
  • Martin Steffen
    • 2
    Email author
  1. 1.Railcomplete ASOsloNorway
  2. 2.Department of InformaticsUniversity of OsloOsloNorway

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