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A dynamical system model of the traffic assignment problem

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  • Jin, Wen-Long

Abstract

User equilibrium is a central concept for studying transportation networks, and one can view it as the result of a dynamical process of drivers' route choice behavior. In this paper, based on a definition of O-D first-in-first-out violation, we propose a new dynamical system model of the route choice behavior at the aggregate, route level for both static and dynamic transportation networks. An equilibrium of such a dynamical system can be a user equilibrium or a partial user equilibrium. We prove that, for static, symmetric traffic assignment problem with fixed or variable demand, only user equilibria are stable for the dynamical system, and the objective function in the mathematical programming formulation [Beckmann, M., McGuire, C.B., Winsten, C.B., 1956. Studies in the Economics of Transportation. Yale University Press, New Haven, Connecticut, also published as Rand-RM-1488-PR, Rand Corporation, Santa Monica, CA, May 12, 1955.] can be considered as the potential energy of the dynamical system. We then present an Euler-based perturbation method for finding user equilibrium and solve two examples for both static and dynamic traffic assignment problems. This new model is simple in form and could be applied to analyze other properties of transportation networks.

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  • 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.
    • Handle: RePEc:eee:transb:v:41:y:2007:i:1:p:32-48
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    6. Minyu Shen & Feng Xiao & Weihua Gu & Hongbo Ye, 2024. "Cognitive Hierarchy in Day-to-day Network Flow Dynamics," Papers 2409.11908, arXiv.org.
    7. Jin, Wen-Long, 2012. "The traffic statics problem in a road network," Transportation Research Part B: Methodological, Elsevier, vol. 46(10), pages 1360-1373.
    8. Guo, Ren-Yong & Huang, Hai-Jun, 2009. "Chaos and bifurcation in dynamical evolution process of traffic assignment with flow “mutation”," Chaos, Solitons & Fractals, Elsevier, vol. 41(3), pages 1150-1157.
    9. 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.
    10. Ernesto Cipriani & Michael Florian & Michael Mahut & Marialisa Nigro, 2010. "Investigating the Efficiency of a Gradient Approximation Approach for the Solution of Dynamic Demand Estimation Problems," Chapters, in: Chris M.J. Tampere & Francesco Viti & Lambertus H. (Ben) Immers (ed.), New Developments in Transport Planning, chapter 18, Edward Elgar Publishing.
    11. Qi, Hang & Jia, Ning & Qu, Xiaobo & He, Zhengbing, 2023. "Investigating day-to-day route choices based on multi-scenario laboratory experiments, Part I: Route-dependent attraction and its modeling," Transportation Research Part A: Policy and Practice, Elsevier, vol. 167(C).
    12. Carey, Malachy & Bar-Gera, Hillel & Watling, David & Balijepalli, Chandra, 2014. "Implementing first-in–first-out in the cell transmission model for networks," Transportation Research Part B: Methodological, Elsevier, vol. 65(C), pages 105-118.
    13. Ye, Hongbo & Xiao, Feng & Yang, Hai, 2021. "Day-to-day dynamics with advanced traveler information," Transportation Research Part B: Methodological, Elsevier, vol. 144(C), pages 23-44.
    14. Ren-Yong Guo & Hai Yang & Hai-Jun Huang & Zhijia Tan, 2016. "Day-to-Day Flow Dynamics and Congestion Control," Transportation Science, INFORMS, vol. 50(3), pages 982-997, August.
    15. Han, Linghui & Sun, Huijun & Wu, Jianjun & Zhu, Chengjuan, 2011. "Day-to-day evolution of the traffic network with Advanced Traveler Information System," Chaos, Solitons & Fractals, Elsevier, vol. 44(10), pages 914-919.
    16. Feng Xiao & Minyu Shen & Zhengtian Xu & Ruijie Li & Hai Yang & Yafeng Yin, 2019. "Day-to-Day Flow Dynamics for Stochastic User Equilibrium and a General Lyapunov Function," Transportation Science, INFORMS, vol. 53(3), pages 683-694, May.
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    18. Wang, Guanfeng & Jia, Hongfei & Feng, Tao & Tian, Jingjing & Wu, Ruiyi & Gao, Heyao & Liu, Chao, 2024. "Modelling the dual dynamic traffic flow evolution with information perception differences between human-driven vehicles and connected autonomous vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 640(C).
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    21. Wen-Long Jin, 2020. "Stable Day-to-Day Dynamics for Departure Time Choice," Transportation Science, INFORMS, vol. 54(1), pages 42-61, January.

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