Document Open Access Logo

The Trickle-In Effect: Modeling Passenger Behavior in Delay Management

Authors Anita Schöbel, Julius Pätzold, Jörg P. Müller

Thumbnail PDF


  • Filesize: 1.11 MB
  • 15 pages

Document Identifiers

Author Details

Anita Schöbel
  • Technical University of Kaiserslautern, Germany
  • Fraunhofer Institute for Industrial Mathematics ITWM, Kaiserslautern, Germany
Julius Pätzold
  • University of Goettingen, Germany
Jörg P. Müller
  • Department of Informatics, Clausthal University of Technology, Germany

Cite AsGet BibTex

Anita Schöbel, Julius Pätzold, and Jörg P. Müller. The Trickle-In Effect: Modeling Passenger Behavior in Delay Management. In 19th Symposium on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2019). Open Access Series in Informatics (OASIcs), Volume 75, pp. 6:1-6:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


Delay management is concerned with making decisions if a train should wait for passengers from delayed trains or if it should depart on time. Models for delay management exist and can be adapted to capacities of stations, capacities of tracks, or respect vehicle and driver schedules, passengers' routes and further constraints. Nevertheless, what has been neglected so far, is that a train cannot depart as planned if passengers from another train trickle in one after another such that the doors of the departing train cannot close. This effect is often observed in real-world, but has not yet been taken into account in delay management. We show the impact of this "trickle-in" effect to departure delays of trains under different conditions. We then modify existing delay management models to take the trickle-in effect into account. This can be done by forbidding certain intervals for departure. We present an integer programming formulation with these additional constraints resulting in a generalization of classic delay management models. We analyze the resulting model and identify parameters with which it can be best approximated by the classical delay management problem. Experimentally, we show that the trickle-in effect has a high impact on the overall delay of public transport systems. We discuss the impact of the trickle-in effect on the objective function value and on the computation time of the delay management problem. We also analyze the trickle-in effect for timetables which have been derived without taking this particular behavioral pattern of passengers into account.

Subject Classification

ACM Subject Classification
  • Applied computing → Transportation
  • Public Transport Planning
  • Delay Management
  • Integer Programming


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


  1. S. Albert, P. Kraus, J.P. Müller, and A. Schöbel. Passenger-induced delay propagation: Agent-based simulation of passengers in rail networks. In Simulation Science, volume 889 of Communications in Computer and Information Science (CCIS), pages 3-23. Springer, 2018. Google Scholar
  2. M. Aschermann, S. Dennisen, P. Kraus, and J.P. Müller. LightJason, a Highly Scalable and Concurrent Agent Framework: Overview and Application (demonstration paper). In M. Dastani, G. Sukthankar, E. Andre, and S. Koenig, editors, Proc. of the 17th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2018), pages 1794-1796, 2018. Google Scholar
  3. R. Bauer and A. Schöbel. Rules of Thumb - Practical online strategies for delay management. Public Transport, 6(1):85-105, 2014. URL:
  4. C. Conte and A. Schöbel. Identifying dependencies among delays. In proceedings of IAROR 2007, 2007. ISBN 978-90-78271-02-4. Google Scholar
  5. L. De Giovanni, G. Heilporn, and M. Labbé. Optimization models for the single delay management problem in public transportation. European Journal of Operational Research, 189(3):762-774, 2008. Google Scholar
  6. T. Dollevoet and D. Huisman. Fast Heuristics for Delay Management with Passenger Rerouting. Public Transport, 6(1-2):67-84, 2014. Google Scholar
  7. T. Dollevoet, D. Huisman, L. Kroon, M. Schmidt, and A. Schöbel. Delay Management including capacities of stations. Transportation Science, 49(2):185-203, 2015. Google Scholar
  8. T. Dollevoet, D. Huisman, L.G. Kroon, L.P. Veelenturf, and J.C.Wagenaar. Application of an iterative framework for real-time railway scheduling. Computers and Operations Research, 78:203-217, 2017. Google Scholar
  9. T. Dollevoet, D. Huisman, M. Schmidt, and A. Schöbel. Delay Management with Rerouting of Passengers. Transportation Science, 46(1):74-89, 2012. Google Scholar
  10. T. Dollevoet, D. Huisman, M. Schmidt, and A. Schöbel. Delay propagation and delay management in transportation networks. In R. Borndörfer et al., editor, Handbook of Optimization in the Railway Industry. Springer, 2018. Google Scholar
  11. M. Goerigk, M. Schachtebeck, and A. Schöbel. Evaluating Line Concepts using Travel Times and Robustness: Simulations with the Lintim toolbox. Public Transport, 5(3), 2013. Google Scholar
  12. M. Goerigk and A. Schöbel. Improving the Modulo Simplex Algorithm for Large-Scale Periodic Timetabling. Computers and Operations Research, 40(5):1363-1370, 2013. Google Scholar
  13. C. Liebchen, M. Proksch, and F.H. Wagner. Performances of Algorithms for Periodic Timetable Optimization. In Computer-aided Systems in Public Transport, pages 151-180. Springer, Heidelberg, 2008. Google Scholar
  14. K. Nachtigall. Periodic Network Optimization and Fixed Interval Timetables. PhD thesis, University of Hildesheim, 1998. Google Scholar
  15. K. Nachtigall and J. Opitz. Solving Periodic Timetable Optimisation Problems by Modulo Simplex Calculations. In Proc. ATMOS, 2008. Google Scholar
  16. J. Pätzold and A. Schöbel. A Matching Approach for Periodic Timetabling. In Marc Goerigk and Renato Werneck, editors, 16th Workshop on Algorithmic Approaches for Transportation Modelling, Optimization, and Systems (ATMOS 2016), volume 54 of OpenAccess Series in Informatics (OASIcs), pages 1-15, Dagstuhl, Germany, 2016. Schloss Dagstuhl-Leibniz-Zentrum für Informatik. URL:
  17. R. Rückert, M. Lemnian, C. Blendinger, S. Rechner, and M. Müller-Hannemann. PANDA: a software tool for improved train dispatching with focus on passenger flows. Public Transport, 9:307-324, 2017. Google Scholar
  18. M. Schachtebeck and A. Schöbel. To wait or not to wait and who goes first? Delay Management with Priority Decisions. Transportation Science, 44(3):307-321, 2010. URL:
  19. A. Schiewe, S. Albert, J. Pätzold, P. Schiewe, A. Schöbel, and J. Schulz. LinTim: An integrated environment for mathematical public transport optimization. Documentation. Technical Report 2018-08, Preprint-Reihe, Institut für Numerische und Angewandte Mathematik, Georg-August-Universität Göttingen, 2018. Google Scholar
  20. M. Schmidt and A. Schöbel. The complexity of integrating routing decisions in public transportation models. Networks, 65(3):228-243, 2015. Google Scholar
  21. A. Schöbel. A Model for the Delay Management Problem based on Mixed-Integer Programming. Electronic Notes in Theoretical Computer Science, 50(1), 2001. Google Scholar
  22. A. Schöbel. Integer Programming approaches for solving the delay management problem. In Algorithmic Methods for Railway Optimization, number 4359 in Lecture Notes in Computer Science, pages 145-170. Springer, 2007. Google Scholar
  23. L. Suhl, C. Biederbick, and N. Kliewer. Design of customer-oriented Dispatching Support for railways. In S. Voß and J. Daduna, editors, Computer-Aided Transit Scheduling, volume 505 of Lecture Notes in Economics and Mathematical systems, pages 365-386. Springer, 2001. 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