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Running times on railway sections with heterogeneous train traffic


  • Huisman, Tijs
  • Boucherie, Richard J.


In contemporary railway traffic, different train services often run on the same track of a railway section. Since these train services generally travel at different speed, this may result in delays due to fast trains being caught behind slower ones. This note investigates these delays developing a stochastic model capturing both scheduled and unscheduled train movements. Running time distributions for each train service can be obtained solving a system of linear differential equations. This system can be solved explicitly when free running times for all train services are deterministic. The mathematical model falls in the class of infinite server resequencing queues, and the results generalise existing results for such queues, allowing dependence between consecutive interarrival times, as well as between interarrival times and service times. A case study of a railway section in the Dutch railway network illustrates the practical value of the model, both for long and short term railway planning.

Suggested Citation

  • Huisman, Tijs & Boucherie, Richard J., 2001. "Running times on railway sections with heterogeneous train traffic," Transportation Research Part B: Methodological, Elsevier, vol. 35(3), pages 271-292, March.
  • Handle: RePEc:eee:transb:v:35:y:2001:i:3:p:271-292

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    Cited by:

    1. Huisman, Tijs & Boucherie, Richard J. & van Dijk, Nico M., 2002. "A solvable queueing network model for railway networks and its validation and applications for the Netherlands," European Journal of Operational Research, Elsevier, vol. 142(1), pages 30-51, October.
    2. Leachman, Robert C. & Jula, Payman, 2012. "Estimating flow times for containerized imports from Asia to the United States through the Western rail network," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 48(1), pages 296-309.
    3. Vromans, Michiel J.C.M. & Dekker, Rommert & Kroon, Leo G., 2006. "Reliability and heterogeneity of railway services," European Journal of Operational Research, Elsevier, vol. 172(2), pages 647-665, July.
    4. Zhang, Jiamin, 2015. "Analysis on line capacity usage for China high speed railway with optimization approach," Transportation Research Part A: Policy and Practice, Elsevier, vol. 77(C), pages 336-349.
    5. 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.
    6. de Kort, A. F. & Heidergott, B. & Ayhan, H., 2003. "A probabilistic (max, +) approach for determining railway infrastructure capacity," European Journal of Operational Research, Elsevier, vol. 148(3), pages 644-661, August.
    7. Fumasoli, Tobias & Bruckmann, Dirk & Weidmann, Ulrich, 2015. "Operation of freight railways in densely used mixed traffic networks – An impact model to quantify changes in freight train characteristics," Research in Transportation Economics, Elsevier, vol. 54(C), pages 15-19.
    8. Krier, Betty & Liu, Chia-Mei & McNamara, Brian & Sharpe, Jerrod, 2014. "Individual freight effects, capacity utilization, and Amtrak service quality," Transportation Research Part A: Policy and Practice, Elsevier, vol. 64(C), pages 163-175.
    9. Mu, Shi & Dessouky, Maged, 2013. "Efficient dispatching rules on double tracks with heterogeneous train traffic," Transportation Research Part B: Methodological, Elsevier, vol. 51(C), pages 45-64.

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