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Modelling Vehicular Traffic Using the Discrete Time Markovian Arrival Process

Author

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  • Attahiru Sule Alfa

    (University of Manitoba, Winnipeg, Manitoba, Canada)

  • Marcel F. Neuts

    (University of Arizona, Tucson, Arizona)

Abstract

A discrete time Markovian Arrival Process which models platooned arrivals in road traffic is presented. It takes into account the bunching of traffic and correlation between headways. Several examples involving different types of probability distributions for interplatoon and intraplatoon headways, and platoon sizes are presented. An application of the MAP to a traffic signal queue is carried out and a numerical example is presented. The example confirmed the intuition that ignoring correlation in the arrival process results in the underestimation of performance measures such as the mean queue length, especially at high traffic intensities.

Suggested Citation

  • Attahiru Sule Alfa & Marcel F. Neuts, 1995. "Modelling Vehicular Traffic Using the Discrete Time Markovian Arrival Process," Transportation Science, INFORMS, vol. 29(2), pages 109-117, May.
    • Handle: RePEc:inm:ortrsc:v:29:y:1995:i:2:p:109-117
    DOI: 10.1287/trsc.29.2.109
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    Cited by:

    1. António Pacheco & Maria Lurdes Simões Simões & Paula Milheiro-Oliveira, 2017. "Queues with Server Vacations as a Model for Pretimed Signalized Urban Traffic," Transportation Science, INFORMS, vol. 51(3), pages 841-851, August.
    2. Neda Mirzaeian & Soo-Haeng Cho & Alan Scheller-Wolf, 2021. "A Queueing Model and Analysis for Autonomous Vehicles on Highways," Management Science, INFORMS, vol. 67(5), pages 2904-2923, May.
    3. 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.
    4. Yang, Qiaoli & Shi, Zhongke & Yu, Shaowei & Zhou, Jie, 2018. "Analytical evaluation of the use of left-turn phasing for single left-turn lane only," Transportation Research Part B: Methodological, Elsevier, vol. 111(C), pages 266-303.
    5. Yang, Qiaoli & Shi, Zhongke, 2018. "The evolution process of queues at signalized intersections under batch arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 413-425.
    6. Long, Keke & Shi, Haotian & Chen, Zhiwei & Liang, Zhaohui & Li, Xiaopeng & de Souza, Felipe, 2024. "Bi-scale car-following model calibration based on corridor-level trajectory," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 186(C).
    7. Attahiru Alfa, 2002. "Discrete time queues and matrix-analytic methods," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 10(2), pages 147-185, December.
    8. Kim, Jungyeol & Sarkar, Saswati & Venkatesh, Santosh S. & Ryerson, Megan Smirti & Starobinski, David, 2020. "An epidemiological diffusion framework for vehicular messaging in general transportation networks," Transportation Research Part B: Methodological, Elsevier, vol. 131(C), pages 160-190.
    9. M.L. Chaudhry & U.C. Gupta, 2003. "Analysis of a finite‐buffer bulk‐service queue with discrete‐Markovian arrival process: D‐MAP/Ga,b/1/N," Naval Research Logistics (NRL), John Wiley & Sons, vol. 50(4), pages 345-363, June.
    10. Banoth Ravi & Manoj Kumar & Yu‐Chen Hu & Shamsul Hassan & Bittu Kumar, 2023. "Stochastic modeling and performance analysis in balancing load and traffic for vehicular ad hoc networks: A review," International Journal of Network Management, John Wiley & Sons, vol. 33(5), September.
    11. Yang, Qiaoli & Shi, Zhongke, 2021. "The queue dynamics of protected/permissive left turns at pre-timed signalized intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    12. Liu, Baoliang & Wen, Yanqing & Qiu, Qingan & Shi, Haiyan & Chen, Jianhui, 2022. "Reliability analysis for multi-state systems under K-mixed redundancy strategy considering switching failure," Reliability Engineering and System Safety, Elsevier, vol. 228(C).
    13. 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.
    14. Yang, Qiaoli & Fu, Xue, 2024. "An extended queueing model for vehicles at signalized intersections considering the platoon correlated arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 635(C).

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