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On the System Optimum Dynamic Traffic Assignment and Earliest Arrival Flow Problems

Author

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  • Hong Zheng

    (Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Arizona 85721)

  • Yi-Chang Chiu

    (Department of Civil Engineering and Engineering Mechanics, University of Arizona, Tucson, Arizona 85721)

  • Pitu B. Mirchandani

    (School of Computing, Informatics and Decision Systems Engineering, Arizona State University, Tempe, Arizona 85287)

Abstract

This paper investigates the cell-transmission model (CTM)-based single destination system optimum dynamic traffic assignment (SO-DTA) problem, focusing attention on a case where the cell properties are time-invariant. We show the backward propagation of congestion in CTM does not affect the optimal arrival flow pattern of SO-DTA, if the fundamental diagram is of triangular/trapezoidal shape as in the CTM. We mathematically prove that the set of earliest arrival flows (EAFs) not constrained by the traffic wave propagation equations obtained on the node-arc network without cell division is a subset of the SO-DTA. This finding leads to a new approach to the SO-DTA that solves the EAF. Such an EAF can be obtained by merely applying static flow techniques and turning the static flows into dynamic flows over time. Therefore, SO-DTA can theoretically be solved with a run time at the link level depending polynomially on log T . We use numerical examples to verify the results and report the computational benefits of the proposed method by solving SO-DTA on a real-world network.

Suggested Citation

  • Hong Zheng & Yi-Chang Chiu & Pitu B. Mirchandani, 2015. "On the System Optimum Dynamic Traffic Assignment and Earliest Arrival Flow Problems," Transportation Science, INFORMS, vol. 49(1), pages 13-27, February.
    • Handle: RePEc:inm:ortrsc:v:49:y:2015:i:1:p:13-27
    DOI: 10.1287/trsc.2013.0485
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    2. Xiaozheng He & Hong Zheng & Srinivas Peeta & Yongfu Li, 2018. "Network Design Model to Integrate Shelter Assignment with Contraflow Operations in Emergency Evacuation Planning," Networks and Spatial Economics, Springer, vol. 18(4), pages 1027-1050, December.
    3. Long, Jiancheng & Wang, Chao & Szeto, W.Y., 2018. "Dynamic system optimum simultaneous route and departure time choice problems: Intersection-movement-based formulations and comparisons," Transportation Research Part B: Methodological, Elsevier, vol. 115(C), pages 166-206.
    4. Jiancheng Long & Wai Yuen Szeto, 2019. "Link-Based System Optimum Dynamic Traffic Assignment Problems in General Networks," Operations Research, INFORMS, vol. 67(1), pages 167-182, January.
    5. Wang, Jian & He, Xiaozheng & Peeta, Srinivas & Wang, Wei, 2022. "Globally convergent line search algorithm with Euler-based step size-determination method for continuous network design problem," Transportation Research Part B: Methodological, Elsevier, vol. 163(C), pages 119-144.

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