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Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models

Author

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  • Rajat Jain

    (Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, Massachusetts 01003)

  • J. Macgregor Smith

    (Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, Massachusetts 01003)

Abstract

In this paper, M/G/C/C state dependent queueing models are proposed for modeling and analyzing vehicular traffic flows. Congestion aspects of traffic flow are represented by introducing state dependent service rates as a function of number of vehicles on each road link. Analytical models for unidirectional and multisource flows are presented. Finally, queueing models to analytically determine the optimal capacity and performance measures of the road links are incorporated into a series of software programs available from the authors.

Suggested Citation

  • Rajat Jain & J. Macgregor Smith, 1997. "Modeling Vehicular Traffic Flow using M/G/C/C State Dependent Queueing Models," Transportation Science, INFORMS, vol. 31(4), pages 324-336, November.
    • Handle: RePEc:inm:ortrsc:v:31:y:1997:i:4:p:324-336
    DOI: 10.1287/trsc.31.4.324
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    Citations

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    Cited by:

    1. Jeffrey P. Kharoufeh & Natarajan Gautam, 2004. "Deriving Link Travel-Time Distributions via Stochastic Speed Processes," Transportation Science, INFORMS, vol. 38(1), pages 97-106, February.
    2. Philip A. Ernst & Søren Asmussen & John J. Hasenbein, 2018. "Stability and busy periods in a multiclass queue with state-dependent arrival rates," Queueing Systems: Theory and Applications, Springer, vol. 90(3), pages 207-224, December.
    3. Ng, ManWo & Khattak, Asad & Talley, Wayne K., 2013. "Modeling the time to the next primary and secondary incident: A semi-Markov stochastic process approach," Transportation Research Part B: Methodological, Elsevier, vol. 58(C), pages 44-57.
    4. 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.
    5. 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.
    6. Georgiadou, Paraskevi S. & Papazoglou, Ioannis A. & Kiranoudis, Chris T. & Markatos, Nikolaos C., 2007. "Modeling emergency evacuation for major hazard industrial sites," Reliability Engineering and System Safety, Elsevier, vol. 92(10), pages 1388-1402.
    7. 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.
    8. LECLUYSE, C. & VAN WOENSEL, Tom & PEREMANS, Herbert, 2007. "Vehicle routing with stochastic time-dependent travel times," Working Papers 2007018, University of Antwerp, Faculty of Business and Economics.
    9. Moshtagh, Mehrdad & Fathali, Jafar & Smith, J. MacGregor, 2018. "The Stochastic Queue Core problem, evacuation networks, and state-dependent queues," European Journal of Operational Research, Elsevier, vol. 269(2), pages 730-748.
    10. Stepanov, Alexander & Smith, James MacGregor, 2009. "Multi-objective evacuation routing in transportation networks," European Journal of Operational Research, Elsevier, vol. 198(2), pages 435-446, October.
    11. Xiao, Jianli & Wang, Zhonghao, 2018. "Traffic speed cloud maps: A new method for analyzing macroscopic traffic flow," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 367-375.
    12. Van Woensel, T. & Kerbache, L. & Peremans, H. & Vandaele, N., 2008. "Vehicle routing with dynamic travel times: A queueing approach," European Journal of Operational Research, Elsevier, vol. 186(3), pages 990-1007, May.
    13. 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.
    14. 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.
    15. Andrew M. Ross, 2009. "Distribution sensitivity in a highway flow model," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 25(6), pages 769-786, November.
    16. Amir Rastpour & Armann Ingolfsson & Bora Kolfal, 2020. "Modeling Yellow and Red Alert Durations for Ambulance Systems," Production and Operations Management, Production and Operations Management Society, vol. 29(8), pages 1972-1991, August.
    17. MacGregor Smith, J. & Cruz, F.R.B., 2014. "M/G/c/c state dependent travel time models and properties," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 560-579.
    18. Cruz, F.R.B. & van Woensel, T. & MacGregor Smith, J. & Lieckens, K., 2010. "On the system optimum of traffic assignment in M/G/c/c state-dependent queueing networks," European Journal of Operational Research, Elsevier, vol. 201(1), pages 183-193, February.
    19. 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.
    20. Hu, Lu & Zhao, Bin & Zhu, Juanxiu & Jiang, Yangsheng, 2019. "Two time-varying and state-dependent fluid queuing models for traffic circulation systems," European Journal of Operational Research, Elsevier, vol. 275(3), pages 997-1019.
    21. Hamad Almujibah & Afaq Khattak & Saleh Alotaibi & Raed Alahmadi & Adil Elhassan & Abdullah Alshahri & Caroline Mongina Matara, 2023. "Two-Level Full Factorial Design Approach for the Analysis of Multi-Lane Highway Section under Saturated and Unsaturated Traffic Flow Conditions," Sustainability, MDPI, vol. 15(12), pages 1-14, June.
    22. J. Macgregor Smith & Wu-Ji Li, 2001. "Quadratic Assignment Problems and M/G/C/C/ State Dependent Network Flows," Journal of Combinatorial Optimization, Springer, vol. 5(4), pages 421-443, December.
    23. 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.
    24. Mehrdad Moshtagh & Jafar Fathali & James MacGregor Smith & Nezam Mahdavi-Amiri, 2019. "Finding an optimal core on a tree network with M/G/c/c state-dependent queues," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 89(1), pages 115-142, February.

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