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Analytical and Scalable Analysis of Transient Tandem Markovian Finite Capacity Queueing Networks

Author

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  • Carolina Osorio

    (Civil and Environmental Engineering Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

  • Jana Yamani

    (Civil and Environmental Engineering Department, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139)

Abstract

This paper proposes an analytical model to approximate the transient aggregate joint queue-length distribution of tandem finite (space) capacity Markovian networks. The methodology combines ideas from transient aggregation-disaggregation techniques as well as transient network decomposition methods. The complexity of the proposed method is linear in the number of queues and is independent of the space capacities of the individual queues. This makes it a suitable approach for the analysis of large-scale networks. The transient joint distributions are validated versus simulation estimates. The model is then used to describe urban traffic dynamics and to address a dynamic traffic signal control problem. The signal plan analysis shows the added value of using joint distributional information, and more generally spatial-temporal between-link dependency information, to enhance urban traffic operations.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:51:y:2017:i:3:p:823-840
    DOI: 10.287/trsc.2015.0629
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    References listed on IDEAS

    as
    1. Carolina Osorio & Krishna Kumar Selvam, 2017. "Simulation-Based Optimization: Achieving Computational Efficiency Through the Use of Multiple Simulators," Transportation Science, INFORMS, vol. 51(2), pages 395-411, May.
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    14. 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.
    15. 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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    Citations

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    Cited by:

    1. Watling, David P. & Hazelton, Martin L., 2018. "Asymptotic approximations of transient behaviour for day-to-day traffic models," Transportation Research Part B: Methodological, Elsevier, vol. 118(C), pages 90-105.
    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. Xiao Chen & Carolina Osorio & Bruno Filipe Santos, 2019. "Simulation-Based Travel Time Reliable Signal Control," Transportation Science, INFORMS, vol. 53(2), pages 523-544, March.
    4. Zhang, Fang & Lu, Jian & Hu, Xiaojian & Meng, Qiang, 2023. "A stochastic dynamic network loading model for mixed traffic with autonomous and human-driven vehicles," Transportation Research Part B: Methodological, Elsevier, vol. 178(C).
    5. Flötteröd, G. & Osorio, C., 2017. "Stochastic network link transmission model," Transportation Research Part B: Methodological, Elsevier, vol. 102(C), pages 180-209.
    6. Xingmin Wang & Zachary Jerome & Zihao Wang & Chenhao Zhang & Shengyin Shen & Vivek Vijaya Kumar & Fan Bai & Paul Krajewski & Danielle Deneau & Ahmad Jawad & Rachel Jones & Gary Piotrowicz & Henry X. L, 2024. "Traffic light optimization with low penetration rate vehicle trajectory data," Nature Communications, Nature, vol. 15(1), pages 1-14, December.
    7. Osorio, Carolina & Punzo, Vincenzo, 2019. "Efficient calibration of microscopic car-following models for large-scale stochastic network simulators," Transportation Research Part B: Methodological, Elsevier, vol. 119(C), pages 156-173.

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