Public Transport

, Volume 6, Issue 1–2, pp 85–105 | Cite as

Rules of thumb: practical online-strategies for delay management

  • Reinhard Bauer
  • Anita SchöbelEmail author
Original Paper


The delay management problem asks how to react to exogenous delays in public railway traffic such that the overall passenger delay is minimized. Such source delays occur in the operational business of public transit and easily make the scheduled timetable infeasible. The delay management problem is a real-time problem further complicated by its online nature. Source delays are not known in advance, hence decisions have to be taken quickly and without exactly knowing the future. This work focuses on online delay management. We enhance established offline models and gain a generic model that is able to cover complex realistic memoryless delay scenarios. We introduce and experimentally evaluate online strategies for delay management that are practical, easily applicable, and robust. Our experiments show that the most promising approach is based on simulation and a learning strategy which is able to deal very well with the wait-depart decisions. Finally, by analyzing the solutions found, we gain interesting insights in the structure of good delay management strategies for real-world railway data.


Delay State Online Phase Online Strategy Delay Management Passenger Delay 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. Bender M, Büttner S, Krumke SO (2013) Online delay management on a single train line: beyond competitive analysis. Public Transp 5(3):243–266CrossRefGoogle Scholar
  2. Berger A, Hoffmann R, Lorenz U, Stiller S (2011) Online railway delay management: hardness, simulation and computation. Simul Model Pract Theory 87(7):616–629CrossRefGoogle Scholar
  3. Buettner S (2013) Online disruption and delay management. PhD thesis, Technical University KaiserslauternGoogle Scholar
  4. Cicerone S, Di Stefano G, Schachtebeck M, Schöbel A (2012) Multi-stage recovery robustness for optimization problems: A new concept for planning under disturbances. Inf Sci 190:107–126CrossRefGoogle Scholar
  5. Corman F, D’Ariano A, Pacciarelli D, Pranzo M (2012) Bi-objective conflict detection and resolution in railway traffic management. Transp Res Part C 20:79–94CrossRefGoogle Scholar
  6. De Giovanni L, Heilporn G, Labbé M (2008) Optimization models for the single delay management problem in public transportation. European Journal of Operational Research 189(3):762–774CrossRefGoogle Scholar
  7. de Vries R, De Schutter B, De Moor B (1998) On max-algebraic models for transportation networks. In: Proceedings of the International Workshop on Discrete Event Systems, p 457–462, Cagliari, ItalyGoogle Scholar
  8. Dollevoet T, Huisman D (2013) Fast heuristics for delay management with passenger rerouting. Public Transp published onlineGoogle Scholar
  9. Dollevoet T, Corman F, D’Ariano A, Huisman D (2012) An iterative optimization framework for delay management and train scheduling. Technical Report EI2012-10, Econometric Institute, Erasmus University RotterdamGoogle Scholar
  10. Dollevoet T, Huisman D, Schmidt M, Schöbel A (2012) Delay management with rerouting of passengers. Transp Sci 46(1):74–89CrossRefGoogle Scholar
  11. Dollevoet T, Schmidt M, Schöbel A (2011) Delay Management including Capacities of Stations. In: Alberto Caprara and Spyros Kontogiannis, editors, 11th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems, volume 20 of OpenAccess Series in Informatics (OASIcs), p 88–99, Dagstuhl, Germany. Schloss Dagstuhl–Leibniz-Zentrum fuer InformatikGoogle Scholar
  12. Gatto M (2007) On the Impact of uncertainty on some optimization problems: combinatorial aspects of delay management and robust online scheduling. PhD thesis, ETH ZürichGoogle Scholar
  13. Gatto M, Glaus B, Jacob R, Peeters L, Widmayer P (2004) Railway delay management: exploring its algorithmic complexity. In: Proceedings of 9th Scandinavian workshop on algorithm theory (SWAT), volume 3111 of Lecture Notes in Computer Science, p 199–211Google Scholar
  14. Gatto M, Jacob R, Peeters L, Schöbel A (2005) The computational complexity of delay management. In: . Kratsch D (ed) Graph-theoretic concepts in computer science: 31st international workshop (WG 2005), volume 3787 of Lecture Notes in Computer ScienceGoogle Scholar
  15. Gatto M, Jacob R, Peeters L, Widmayer P (2007) On-line delay management on a single train line. In: Algorithmic methods for railway optimization, number 4359 in Lecture Notes in Computer Science, Springer, Heidelberg, p 306–320Google Scholar
  16. Ginkel A, Schöbel A (2007) To wait or not to wait? The bicriteria delay management problem in public transportation. Transp Sci 41(4):527–538CrossRefGoogle Scholar
  17. Goerigk M, Harbering J, Schöbel A (2013a) LinTim—integrated optimization in public transportation. Homepage. see
  18. Goerigk M, Schachtebeck M, Schöbel A (2013b) Evaluating line concepts using travel times and robustness: Simulations with the lintim toolbox. Public Transp 5:267–284CrossRefGoogle Scholar
  19. Goverde RMP (1998) The max-plus algebra approach to railway timetable design. In: Computers in railways VI: Proceedings of the 6th international conference on computer aided design, manufacture and operations in the railway and other advanced mass transit systems, Lisbon, 1998, p 339–350Google Scholar
  20. Kliewer N, Suhl L (2011) A note on the online nature of the railway delay management problem. Networks 57(1):28–37CrossRefGoogle Scholar
  21. Krumke S, Thielen C, Zeck C (2011) Extensions to online delay management on a single train line: new bounds for delay minimization and profit maximization. Mathematical Methods of Operations Research 74(1):53–75CrossRefGoogle Scholar
  22. Liebchen C, Schachtebeck M, Schöbel A, Stiller S, Prigge A (2010) Computing delay-resistant railway timetables. Comput Oper Res 37:857–868CrossRefGoogle Scholar
  23. Schachtebeck M (2010) Delay management in public transportation: capacities, robustness, and integration. PhD thesis, Universität GöttingenGoogle Scholar
  24. Schachtebeck M, Schöbel A (2010) To wait or not to wait and who goes first? Delay management with priority decisions. Transp Sci 44(3):307–321CrossRefGoogle Scholar
  25. Schöbel A (2001) A model for the delay management problem based on mixed-integer programming. Electronic notes in theoretical computer science, 50(1)Google Scholar
  26. Schöbel A (2006) Optimization in public transportation. Stop location, delay management and tariff planning from a customer-oriented point of view. Optimization and Its applications. Springer, New YorkGoogle Scholar
  27. Schöbel A (2007) Integer programming approaches for solving the delay management problem. In: Algorithmic methods for railway optimization, number 4359 in Lecture Notes in Computer Science, Springer, Heidelberg, p 145–170Google Scholar
  28. Schöbel A (2009) Capacity constraints in delay management. Public Transp 1(2):135–154CrossRefGoogle Scholar
  29. Schmidt M (2012) Integrating routing decisions in network problems. PhD thesis, Universität GöttingenGoogle Scholar
  30. Schmidt M (2013) Simultaneous optimization of delay management decisions and passenger routes. Public Transp 5(1):125–147CrossRefGoogle Scholar
  31. Suhl L, Mellouli T, Biederbick C, Goecke J (2001) Managing and preventing delays in railway traffic by simulation and optimization. In: Pursula M, Niittymäki (eds) Mathematical methods on optimization in transportation systems, Kluwer, p 3–16Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.ABB Corporate ResearchLadenburgGermany
  2. 2.Institute for Numerical and Applied MathematicsGeorg-August UniversityGöttingenGermany

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