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A discrete time dynamic flow model and a formulation and solution method for dynamic route choice

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  • Jang, Wonjae
  • Ran, Bin
  • Choi, Keechoo

Abstract

This paper considers the ideal dynamic user optimal (DUO) route choice problem using a route-based variational inequality approach. A discrete time dynamic flow model is developed, which uses link travel time functions to determine time-dependent network states. The proposed flow model is built on discrete time flow variables, to eliminate the discretization process of continuous time based models. Continuity of route travel time functions is proven to establish the existence of a solution, on the condition that the link travel time functions are continuous. Furthermore, flow dispersion and concentration can be simulated, which is expected to enhance the ability of capturing dynamics of traffic movements. A variational inequality formulation based on an alternative cost mapping is proposed, which is derived from a route swapping heuristic approach. As a solution method, the projection-based approach is used since the route travel time functions in our model are not smooth. To increase the performance of the projection-based methods, an efficient implementation of the projection operation is developed. Computational experiences with two example networks are provided to illustrate the model.

Suggested Citation

  • Jang, Wonjae & Ran, Bin & Choi, Keechoo, 2005. "A discrete time dynamic flow model and a formulation and solution method for dynamic route choice," Transportation Research Part B: Methodological, Elsevier, vol. 39(7), pages 593-620, August.
    • Handle: RePEc:eee:transb:v:39:y:2005:i:7:p:593-620
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    Cited by:

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    2. Lu, Chung-Cheng & Mahmassani, Hani S. & Zhou, Xuesong, 2009. "Equivalent gap function-based reformulation and solution algorithm for the dynamic user equilibrium problem," Transportation Research Part B: Methodological, Elsevier, vol. 43(3), pages 345-364, March.
    3. Lu, Gongyuan & Nie, Yu(Marco) & Liu, Xiaobo & Li, Denghui, 2019. "Trajectory-based traffic management inside an autonomous vehicle zone," Transportation Research Part B: Methodological, Elsevier, vol. 120(C), pages 76-98.
    4. František Kolovský & Ivana Kolingerová, 2022. "The Piecewise Constant/Linear Solution for Dynamic User Equilibrium," Networks and Spatial Economics, Springer, vol. 22(4), pages 737-765, December.
    5. Long, Jiancheng & Szeto, W.Y. & Gao, Ziyou & Huang, Hai-Jun & Shi, Qin, 2016. "The nonlinear equation system approach to solving dynamic user optimal simultaneous route and departure time choice problems," Transportation Research Part B: Methodological, Elsevier, vol. 83(C), pages 179-206.
    6. 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.
    7. Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    8. Han, Ke & Friesz, Terry L. & Szeto, W.Y. & Liu, Hongcheng, 2015. "Elastic demand dynamic network user equilibrium: Formulation, existence and computation," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 183-209.
    9. Wang, Dong & Liao, Feixiong & Gao, Ziyou & Rasouli, Soora & Huang, Hai-Jun, 2020. "Tolerance-based column generation for boundedly rational dynamic activity-travel assignment in large-scale networks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 141(C).

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