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A Queueing Theory Model of Nonstationary Traffic Flow

Author

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  • Dirk Heidemann

    (Heilbronn University of AppIied Sciences, Institute of Applied Research, Daimlerstraβe 35, D-74653 Künzelsau, Germany)

Abstract

The queueing-theoretical model for stationary traffic flow developed in a former paper is extended and modified for nonstationary flow. In particular it is shown how speed-flow-density relationships under nonstationary conditions may deviate from those obtained for stationary conditions. It is shown how the wide scatter which is often observed with empirical speed-flow-density data can be explained by nonstationarity. Furthermore, hysteresis loops, which may show up in speed-flow-density relationships, are interpreted by means of nonstationarity.

Suggested Citation

  • Dirk Heidemann, 2001. "A Queueing Theory Model of Nonstationary Traffic Flow," Transportation Science, INFORMS, vol. 35(4), pages 405-412, November.
    • Handle: RePEc:inm:ortrsc:v:35:y:2001:i:4:p:405-412
    DOI: 10.1287/trsc.35.4.405.10430
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    Cited by:

    1. Pedro Cesar Lopes Gerum & Andrew Reed Benton & Melike Baykal-Gürsoy, 2019. "Traffic density on corridors subject to incidents: models for long-term congestion management," EURO Journal on Transportation and Logistics, Springer;EURO - The Association of European Operational Research Societies, vol. 8(5), pages 795-831, December.
    2. Jing Lu & Carolina Osorio, 2018. "A Probabilistic Traffic-Theoretic Network Loading Model Suitable for Large-Scale Network Analysis," Service Science, INFORMS, vol. 52(6), pages 1509-1530, December.
    3. Osorio, Carolina & Wang, Carter, 2017. "On the analytical approximation of joint aggregate queue-length distributions for traffic networks: A stationary finite capacity Markovian network approach," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 305-339.
    4. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    5. Yeon, Jiyoun & Elefteriadou, Lily & Lawphongpanich, Siriphong, 2008. "Travel time estimation on a freeway using Discrete Time Markov Chains," Transportation Research Part B: Methodological, Elsevier, vol. 42(4), pages 325-338, May.
    6. Baykal-Gürsoy, M. & Xiao, W. & Ozbay, K., 2009. "Modeling traffic flow interrupted by incidents," European Journal of Operational Research, Elsevier, vol. 195(1), pages 127-138, May.
    7. Lan Lu & Zheng Zhu & Pengfei Guo & Qiao‐Chu He, 2022. "Service Operations for Mixed Autonomous Paradigm: Lane Design and Subsidy," Production and Operations Management, Production and Operations Management Society, vol. 31(4), pages 1595-1612, April.
    8. Niek Baer & Richard J. Boucherie & Jan-Kees C. W. van Ommeren, 2019. "Threshold Queueing to Describe the Fundamental Diagram of Uninterrupted Traffic," Transportation Science, INFORMS, vol. 53(2), pages 585-596, March.
    9. Linsen Chong & Carolina Osorio, 2018. "A Simulation-Based Optimization Algorithm for Dynamic Large-Scale Urban Transportation Problems," Transportation Science, INFORMS, vol. 52(3), pages 637-656, June.
    10. Carolina Osorio & Jana Yamani, 2017. "Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks," Transportation Science, INFORMS, vol. 51(3), pages 823-840, August.
    11. Drichoutis, Andreas C. & Grimm, Veronika & Karakostas, Alexandros, 2020. "Bribing to Queue-Jump: An experiment on cultural differences in bribing attitudes among Greeks and Germans," MPRA Paper 102775, University Library of Munich, Germany.
    12. Osorio, Carolina & Flötteröd, Gunnar & Bierlaire, Michel, 2011. "Dynamic network loading: A stochastic differentiable model that derives link state distributions," Transportation Research Part B: Methodological, Elsevier, vol. 45(9), pages 1410-1423.

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