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Modelling train delays with q-exponential functions

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  • Briggs, Keith
  • Beck, Christian

Abstract

We demonstrate that the distribution of train delays on the British railway network is accurately described by q-exponential functions. We explain this by constructing an underlying superstatistical model.

Suggested Citation

  • Briggs, Keith & Beck, Christian, 2007. "Modelling train delays with q-exponential functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 378(2), pages 498-504.
    • Handle: RePEc:eee:phsmap:v:378:y:2007:i:2:p:498-504
    DOI: 10.1016/j.physa.2006.11.084
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    References listed on IDEAS

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    1. Chavanis, Pierre-Henri, 2006. "Coarse-grained distributions and superstatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 359(C), pages 177-212.
    2. Abul-Magd, A.Y., 2006. "Superstatistics in random matrix theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 41-54.
    3. Beck, Christian, 2004. "Generalized statistical mechanics of cosmic rays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 173-181.
    4. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
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    Cited by:

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    2. Bergström, Anna & Krüger, Niclas A., 2013. "Modeling passenger train delay distributions: evidence and implications," Working papers in Transport Economics 2013:3, CTS - Centre for Transport Studies Stockholm (KTH and VTI).
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    7. Lubashevsky, Ihor & Friedrich, Rudolf & Heuer, Andreas & Ushakov, Andrey, 2009. "Generalized superstatistics of nonequilibrium Markovian systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(21), pages 4535-4550.
    8. 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.
    9. M. Finger & A. Haller & S. Strube Martins & U. Trinkner, 2014. "Integrated Timetables for Railway Passenger Transport Services," Competition and Regulation in Network Industries, Intersentia, vol. 15(1), pages 78-107, March.
    10. Bercher, J.-F. & Vignat, C., 2008. "A new look at q-exponential distributions via excess statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(22), pages 5422-5432.
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    12. 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).
    13. Eva Nedeliakova & Maria Hudakova & Matej Masar & Lenka Lizbetinova & Renata Stasiak-Betlejewska & Peter Šulko, 2020. "Sustainability of Railway Undertaking Services with Lean Philosophy in Risk Management—Case Study," Sustainability, MDPI, vol. 12(13), pages 1-28, June.
    14. Butusov, Denis N. & Karimov, Artur I. & Pyko, Nikita S. & Pyko, Svetlana A. & Bogachev, Mikhail I., 2018. "Discrete chaotic maps obtained by symmetric integration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 955-970.
    15. Vasile Preda & Luigi-Ionut Catana, 2021. "Tsallis Log-Scale-Location Models. Moments, Gini Index and Some Stochastic Orders," Mathematics, MDPI, vol. 9(11), pages 1-22, May.
    16. Ewin Sánchez, 2023. "Q-Weibull distribution to explain the PM2.5 air pollution concentration in Santiago de Chile," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(8), pages 1-8, August.
    17. Bogachev, Mikhail I. & Kuzmenko, Alexander V. & Markelov, Oleg A. & Pyko, Nikita S. & Pyko, Svetlana A., 2023. "Approximate waiting times for queuing systems with variable long-term correlated arrival rates," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 614(C).
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