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Day-to-Day Flow Dynamics and Congestion Control

Author

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  • Ren-Yong Guo

    (College of Computer Science, Inner Mongolia University, 010021 Hohhot, China)

  • Hai Yang

    (Department of Civil and Environmental Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong)

  • Hai-Jun Huang

    (School of Economics and Management, Beihang University, 100191 Beijing, China)

  • Zhijia Tan

    (School of Management, Huazhong University of Science and Technology, 430074 Wuhan, China)

Abstract

For a predetermined set of an upper bound of link flows, this paper proposes a price-based congestion control scheme for achieving such a restraint target of traffic flow that evolves from day to day. On each day, drivers have to pay a toll selected from a feasible set. The tolls on each day are determined by the link flows and toll charges on the previous day and the predetermined upper bound of link flows. Several properties of the dynamical system model with the control scheme are analyzed, including the invariance of its evolutionary trajectories; the equivalence between its stationary state and user equilibrium under toll charge; the uniqueness, existence, and boundedness of its stationary state; and the convergence of its evolutionary trajectories. A special case of the model and implementation of the control scheme for several alternative targets are also given. Finally, application of the model to a traffic network is demonstrated with a numerical example. The study is helpful for better understanding the mechanism of congestion control under day-to-day traffic flow dynamics.

Suggested Citation

  • 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.
    • Handle: RePEc:inm:ortrsc:v:50:y:2016:i:3:p:982-997
    DOI: 10.1287/trsc.2015.0596
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