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Time-dependent Ginzburg–Landau equation in a car-following model considering the driver’s physical delay

Author

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  • Ge, Hong-xia
  • Meng, Xiang-pei
  • Cheng, Rong-jun
  • Lo, Siu-Ming

Abstract

In this paper, an extended car-following model considering the delay of the driver’s response in sensing headway is proposed to describe the traffic jam. It is shown that the stability region decreases when the driver’s physical delay in sensing headway increases. The phase transition among the freely moving phase, the coexisting phase, and the uniformly congested phase occurs below the critical point. By applying the reductive perturbation method, we get the time-dependent Ginzburg–Landau (TDGL) equation from the car-following model to describe the transition and critical phenomenon in traffic flow. We show the connection between the TDGL equation and the mKdV equation describing the traffic jam.

Suggested Citation

  • Ge, Hong-xia & Meng, Xiang-pei & Cheng, Rong-jun & Lo, Siu-Ming, 2011. "Time-dependent Ginzburg–Landau equation in a car-following model considering the driver’s physical delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(20), pages 3348-3353.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:20:p:3348-3353
    DOI: 10.1016/j.physa.2011.04.033
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    Citations

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    Cited by:

    1. Sun, Dihua & Chen, Dong & Zhao, Min & Liu, Weining & Zheng, Linjiang, 2018. "Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 293-307.
    2. Yang, Da & Jin, Peter (Jing) & Pu, Yun & Ran, Bin, 2014. "Stability analysis of the mixed traffic flow of cars and trucks using heterogeneous optimal velocity car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 395(C), pages 371-383.
    3. Ma, Guangyi & Li, Keping, 2024. "Analysis and simulation of vehicle following behavior with consideration of multiple time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).

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