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Stochastic delay propagation in railway networks and phase-type distributions

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  • Meester, Ludolf E.
  • Muns, Sander

Abstract

It is difficult to analyse stochastic models for the propagation of delays in railway networks. It seems that the choice is between very global mathematical (queueing) models at one extreme and simulation models at the other. In this paper we discuss a (fairly general but not too detailed) model for delay propagation and show that in a world of so-called phase-type distributions it is possible to derive secondary delay distributions from primary delay distributions. We shall explain why phase-type distributions and the delay propagation model are suited for each other and show by an example that it is possible to develop algorithms that analyse such networks.

Suggested Citation

  • Meester, Ludolf E. & Muns, Sander, 2007. "Stochastic delay propagation in railway networks and phase-type distributions," Transportation Research Part B: Methodological, Elsevier, vol. 41(2), pages 218-230, February.
    • Handle: RePEc:eee:transb:v:41:y:2007:i:2:p:218-230
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    1. A. Higgins & E. Kozan, 1998. "Modeling Train Delays in Urban Networks," Transportation Science, INFORMS, vol. 32(4), pages 346-357, November.
    2. Carey, Malachy & Kwiecinski, Andrzej, 1994. "Stochastic approximation to the effects of headways on knock-on delays of trains," Transportation Research Part B: Methodological, Elsevier, vol. 28(4), pages 251-267, August.
    3. Carey, Malachy & Kwiecinski, Andrzej, 1995. "Properties of expected costs and performance measures in stochastic models of scheduled transport," European Journal of Operational Research, Elsevier, vol. 83(1), pages 182-199, May.
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    Cited by:

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    2. Chao Wen & Zhongcan Li & Javad Lessan & Liping Fu & Ping Huang & Chaozhe Jiang, 2017. "Statistical investigation on train primary delay based on real records: evidence from Wuhan–Guangzhou HSR," International Journal of Rail Transportation, Taylor & Francis Journals, vol. 5(3), pages 170-189, July.
    3. Maosheng Li & Zhengqiu Liu & Yonghong Zhang & Weijun Liu & Feng Shi, 2017. "Distribution analysis of train interval journey time employing the censored model with shifting character," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(4), pages 715-733, March.
    4. Chao Wen & Weiwei Mou & Ping Huang & Zhongcan Li, 2020. "A predictive model of train delays on a railway line," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(3), pages 470-488, April.
    5. Zhongcan Li & Ping Huang & Chao Wen & Yixiong Tang & Xi Jiang, 2020. "Predictive models for influence of primary delays using high‐speed train operation records," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(8), pages 1198-1212, December.
    6. Gardner, Clara Brimnes & Nielsen, Sara Dorthea & Eltved, Morten & Rasmussen, Thomas Kjær & Nielsen, Otto Anker & Nielsen, Bo Friis, 2021. "Calculating conditional passenger travel time distributions in mixed schedule- and frequency-based public transport networks using Markov chains," Transportation Research Part B: Methodological, Elsevier, vol. 152(C), pages 1-17.
    7. Hangfei Huang & Keping Li & Paul Schonfeld, 2018. "Real-time energy-saving metro train rescheduling with primary delay identification," PLOS ONE, Public Library of Science, vol. 13(2), pages 1-22, February.
    8. Agbelie, Bismark & Libnao, Kathleen, 2018. "Unobserved heterogeneity analysis of rail transit incident delays," Transportation Research Part A: Policy and Practice, Elsevier, vol. 117(C), pages 39-43.
    9. Huang, Ping & Wen, Chao & Fu, Liping & Lessan, Javad & Jiang, Chaozhe & Peng, Qiyuan & Xu, Xinyue, 2020. "Modeling train operation as sequences: A study of delay prediction with operation and weather data," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).
    10. Nan Cao & Tao Tang & Chunhai Gao, 2020. "A Study of Hindrance-Caused Unscheduled Waiting Time in Railway Systems," Sustainability, MDPI, vol. 12(14), pages 1-17, July.
    11. PeCoy, Michael D. & Redmond, Michael A., 2023. "Flight reliability during periods of high uncertainty," Journal of Air Transport Management, Elsevier, vol. 106(C).
    12. Harshad Khadilkar, 2017. "Data-Enabled Stochastic Modeling for Evaluating Schedule Robustness of Railway Networks," Transportation Science, INFORMS, vol. 51(4), pages 1161-1176, November.
    13. 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.
    14. Huang, Ping & Guo, Jingwei & Liu, Shu & Corman, Francesco, 2024. "Explainable train delay propagation: A graph attention network approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 184(C).
    15. Wei, Dali & Liu, Hongchao & Qin, Yong, 2015. "Modeling cascade dynamics of railway networks under inclement weather," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 80(C), pages 95-122.

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