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Graphical solution and continuum approximation for the single destination dynamic user equilibrium problem

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  • Laval, Jorge A.

Abstract

This paper studies the user optimum dynamic traffic assignment in a network consisting of a congested freeway section connected to a surface street grid via capacitated off-ramps. It is shown that although the network is simple, it is in general complicated to obtain the optimum solution analytically because (i) it has two different alternating diversion patterns and (ii) it can only be obtained sequentially in time. A simplified graphical solution method is proposed to cope with (i) but the method remains sequential. Finally, a continuum approximation is proposed that enables finding closed-form solutions without the above limitations.

Suggested Citation

  • Laval, Jorge A., 2009. "Graphical solution and continuum approximation for the single destination dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(1), pages 108-118, January.
    • Handle: RePEc:eee:transb:v:43:y:2009:i:1:p:108-118
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    References listed on IDEAS

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    1. Jin, Wen-Long, 2007. "A dynamical system model of the traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 41(1), pages 32-48, January.
    2. Peeta, Srinivas & Zhou, Chao, 2006. "Stochastic quasi-gradient algorithm for the off-line stochastic dynamic traffic assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 40(3), pages 179-206, March.
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    6. Lo, Hong K. & Szeto, W. Y., 2002. "A cell-based variational inequality formulation of the dynamic user optimal assignment problem," Transportation Research Part B: Methodological, Elsevier, vol. 36(5), pages 421-443, June.
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    Cited by:

    1. Laval, Jorge A. & Cho, Hyun W. & Muñoz, Juan C. & Yin, Yafeng, 2015. "Real-time congestion pricing strategies for toll facilities," Transportation Research Part B: Methodological, Elsevier, vol. 71(C), pages 19-31.
    2. Laval, Jorge A. & Leclercq, Ludovic & Chiabaut, Nicolas, 2018. "Minimal parameter formulations of the dynamic user equilibrium using macroscopic urban models: Freeway vs city streets revisited," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 676-686.
    3. Cortina, Mélanie & Chiabaut, Nicolas & Leclercq, Ludovic, 2023. "Fostering synergy between transit and Autonomous Mobility-on-Demand systems: A dynamic modeling approach for the morning commute problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 170(C).
    4. Aghamohammadi, Rafegh & Laval, Jorge A., 2020. "Dynamic traffic assignment using the macroscopic fundamental diagram: A Review of vehicular and pedestrian flow models," Transportation Research Part B: Methodological, Elsevier, vol. 137(C), pages 99-118.
    5. Zhao, Chuan-Lin & Leclercq, Ludovic, 2018. "Graphical solution for system optimum dynamic traffic assignment with day-based incentive routing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 117(PA), pages 87-100.

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