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Stochastic improvement of cyclic railway timetables

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  • Kroon, Leo
  • Maróti, Gábor
  • Helmrich, Mathijn Retel
  • Vromans, Michiel
  • Dekker, Rommert

Abstract

Real-time railway operations are subject to stochastic disturbances. Thus a timetable should be designed in such a way that it can cope with these disturbances as well as possible. For that purpose, a timetable usually contains time supplements in several process times and buffer times between pairs of consecutive trains. This paper describes a Stochastic Optimization Model that can be used to allocate the time supplements and the buffer times in a given timetable in such a way that the timetable becomes maximally robust against stochastic disturbances. The Stochastic Optimization Model was tested on several instances of NS Reizigers, the main operator of passenger trains in the Netherlands. Moreover, a timetable that was computed by the model was operated in practice in a timetable experiment on the so-called "Zaanlijn". The results show that the average delays of trains can often be reduced significantly by applying relatively small modifications to a given timetable.

Suggested Citation

  • Kroon, Leo & Maróti, Gábor & Helmrich, Mathijn Retel & Vromans, Michiel & Dekker, Rommert, 2008. "Stochastic improvement of cyclic railway timetables," Transportation Research Part B: Methodological, Elsevier, vol. 42(6), pages 553-570, July.
  • Handle: RePEc:eee:transb:v:42:y:2008:i:6:p:553-570
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Cacchiani, Valentina & Toth, Paolo, 2012. "Nominal and robust train timetabling problems," European Journal of Operational Research, Elsevier, vol. 219(3), pages 727-737.
    2. repec:eee:transb:v:105:y:2017:i:c:p:144-173 is not listed on IDEAS
    3. Lee, Yusin & Lu, Li-Sin & Wu, Mei-Ling & Lin, Dung-Ying, 2017. "Balance of efficiency and robustness in passenger railway timetables," Transportation Research Part B: Methodological, Elsevier, vol. 97(C), pages 142-156.
    4. Kroon, L.G. & Peeters, L.W.P. & Wagenaar, J.C. & Zuidwijk, R.A., 2012. "Flexible Connections in PESP Models for Cyclic Passenger Railway Timetabling," ERIM Report Series Research in Management ERS-2012-008-LIS, Erasmus Research Institute of Management (ERIM), ERIM is the joint research institute of the Rotterdam School of Management, Erasmus University and the Erasmus School of Economics (ESE) at Erasmus University Rotterdam.
    5. Cacchiani, Valentina & Caprara, Alberto & Toth, Paolo, 2010. "Scheduling extra freight trains on railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 215-231, February.
    6. Li, Xiang & Lo, Hong K., 2014. "An energy-efficient scheduling and speed control approach for metro rail operations," Transportation Research Part B: Methodological, Elsevier, vol. 64(C), pages 73-89.
    7. Niu, Huimin & Zhou, Xuesong & Gao, Ruhu, 2015. "Train scheduling for minimizing passenger waiting time with time-dependent demand and skip-stop patterns: Nonlinear integer programming models with linear constraints," Transportation Research Part B: Methodological, Elsevier, vol. 76(C), pages 117-135.
    8. repec:eee:transb:v:101:y:2017:i:c:p:228-244 is not listed on IDEAS
    9. Hassini, Elkafi & Verma, Manish, 2016. "Disruption risk management in railroad networks: An optimization-based methodology and a case studyAuthor-Name: Azad, Nader," Transportation Research Part B: Methodological, Elsevier, vol. 85(C), pages 70-88.
    10. Robenek, Tomáš & Maknoon, Yousef & Azadeh, Shadi Sharif & Chen, Jianghang & Bierlaire, Michel, 2016. "Passenger centric train timetabling problem," Transportation Research Part B: Methodological, Elsevier, vol. 89(C), pages 107-126.
    11. Mulder, J. & van Jaarsveld, W.L. & Dekker, R., 2016. "Simultaneous optimization of speed and buffer times for robust transportation systems," Econometric Institute Research Papers EI2016-36, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    12. Sparing, Daniel & Goverde, Rob M.P., 2017. "A cycle time optimization model for generating stable periodic railway timetables," Transportation Research Part B: Methodological, Elsevier, vol. 98(C), pages 198-223.
    13. Kang, Liujiang & Wu, Jianjun & Sun, Huijun & Zhu, Xiaoning & Gao, Ziyou, 2015. "A case study on the coordination of last trains for the Beijing subway network," Transportation Research Part B: Methodological, Elsevier, vol. 72(C), pages 112-127.
    14. Yang, Lixing & Qi, Jianguo & Li, Shukai & Gao, Yuan, 2016. "Collaborative optimization for train scheduling and train stop planning on high-speed railways," Omega, Elsevier, vol. 64(C), pages 57-76.
    15. Yang, Lixing & Zhou, Xuesong & Gao, Ziyou, 2014. "Credibility-based rescheduling model in a double-track railway network: a fuzzy reliable optimization approach," Omega, Elsevier, vol. 48(C), pages 75-93.
    16. Jovanović, Predrag & Kecman, Pavle & Bojović, Nebojša & Mandić, Dragomir, 2017. "Optimal allocation of buffer times to increase train schedule robustness," European Journal of Operational Research, Elsevier, vol. 256(1), pages 44-54.
    17. Sels, P. & Dewilde, T. & Cattrysse, D. & Vansteenwegen, P., 2016. "Reducing the passenger travel time in practice by the automated construction of a robust railway timetable," Transportation Research Part B: Methodological, Elsevier, vol. 84(C), pages 124-156.
    18. Vansteenwegen, Pieter & Dewilde, Thijs & Burggraeve, Sofie & Cattrysse, Dirk, 2016. "An iterative approach for reducing the impact of infrastructure maintenance on the performance of railway systems," European Journal of Operational Research, Elsevier, vol. 252(1), pages 39-53.
    19. Cordone, Roberto & Redaelli, Francesco, 2011. "Optimizing the demand captured by a railway system with a regular timetable," Transportation Research Part B: Methodological, Elsevier, vol. 45(2), pages 430-446, February.
    20. Yang, Xin & Chen, Anthony & Ning, Bin & Tang, Tao, 2017. "Bi-objective programming approach for solving the metro timetable optimization problem with dwell time uncertainty," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 97(C), pages 22-37.

    More about this item

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • M - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics

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