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Stochastic dynamics of a discrete-time car-following model and its time-delayed feedback control

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  • Meng, Jingwei
  • Jin, Yanfei
  • Xu, Meng

Abstract

In this paper, a discrete-time optimal velocity model (DOVM) is presented by discretizing continuous car-following model into a difference equation. Considering the influences of stochastic disturbance on DOVM, the stochastic stability is studied by using Z-transform and Routh criterion. The theoretical expressions of the velocity oscillation amplitude and stability conditions are derived from the expected variance of the velocity variable. To stabilize the unstable traffic flow in DOVM, the time-delayed feedback control strategies are proposed by considering velocity difference and displacement–velocity–acceleration difference, respectively. Then, the stochastic stability of controlled DOVM and the choose of control parameters are provided. The numerical simulations for different traffic scenes indicate that the proposed control strategies can improve system stability and suppress traffic jams effectively. Based on the actual traffic data provided by NGSIM and quantum particle swarm algorithm, the parameters in DOVM are calibrated to optimize the car-following model. Furthermore, the proposed control methods are verified through the actual measured traffic data.

Suggested Citation

  • Meng, Jingwei & Jin, Yanfei & Xu, Meng, 2023. "Stochastic dynamics of a discrete-time car-following model and its time-delayed feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 610(C).
    • Handle: RePEc:eee:phsmap:v:610:y:2023:i:c:s0378437122009657
    DOI: 10.1016/j.physa.2022.128407
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    References listed on IDEAS

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    1. Zhang, Yicai & Xue, Yu & Zhang, Peng & Fan, Deli & di He, Hong, 2019. "Bifurcation analysis of traffic flow through an improved car-following model considering the time-delayed velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 133-140.
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    Cited by:

    1. Kun Zhang & Yu Xue & Hao-Jie Luo & Qiang Zhang & Yuan Tang & Bing-Ling Cen, 2023. "Cyber-attacks on the optimal velocity and its variation by bifurcation analyses," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 96(12), pages 1-19, December.

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