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Modeling traffic flow interrupted by incidents

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  • Baykal-Gürsoy, M.
  • Xiao, W.
  • Ozbay, K.

Abstract

A steady-state M/M/c queueing system under batch service interruptions is introduced to model the traffic flow on a roadway link subject to incidents. When a traffic incident happens, either all lanes or part of a lane is closed to the traffic. As such, we model these interruptions either as complete service disruptions where none of the servers work or partial failures where servers work at a reduced service rate. We analyze this system in steady-state and present a scheme to obtain the stationary number of vehicles on a link. For those links with large c values, the closed-form solution of M/M/[infinity] queues under batch service interruptions can be used as an approximation. We present simulation results that show the validity of the queueing models in the computation of average travel times.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:127-138
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    3. Yona Elbaum & Alexander Novoselsky & Evgeny Kagan, 2022. "A Queueing Model for Traffic Flow Control in the Road Intersection," Mathematics, MDPI, vol. 10(21), pages 1-15, October.
    4. A. Krishnamoorthy & P. Pramod & S. Chakravarthy, 2014. "Queues with interruptions: a survey," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 290-320, April.
    5. L. G. Afanasyeva, 2020. "Asymptotic Analysis of Queueing Models Based on Synchronization Method," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1417-1438, December.
    6. Vishal Mandal & Abdul Rashid Mussah & Peng Jin & Yaw Adu-Gyamfi, 2020. "Artificial Intelligence-Enabled Traffic Monitoring System," Sustainability, MDPI, vol. 12(21), pages 1-21, November.
    7. Wenwen Li & Alexander Goldenshluger, 2024. "Adaptive minimax estimation of service time distribution in the $$M_t/G/\infty $$ M t / G / ∞ queue from departure data," Queueing Systems: Theory and Applications, Springer, vol. 108(1), pages 81-123, October.
    8. Gao, Jingqin & Zuo, Fan & Ozbay, Kaan & Hammami, Omar & Barlas, Murat Ledin, 2022. "A new curb lane monitoring and illegal parking impact estimation approach based on queueing theory and computer vision for cameras with low resolution and low frame rate," Transportation Research Part A: Policy and Practice, Elsevier, vol. 162(C), pages 137-154.
    9. 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.
    10. Larisa Afanasyeva & Ekaterina Bulinskaya, 2013. "Asymptotic Analysis of Traffic Lights Performance Under Heavy Traffic Assumption," Methodology and Computing in Applied Probability, Springer, vol. 15(4), pages 935-950, December.
    11. Jianjun Li & Liwei Liu & Tao Jiang, 2018. "Analysis of an M/G/1 queue with vacations and multiple phases of operation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 87(1), pages 51-72, February.
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