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Density waves in a traffic flow model with reaction-time delay

Author

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  • Yu, Lei
  • Li, Tong
  • Shi, Zhong-Ke

Abstract

Density waves are investigated analytically and numerically in the optimal velocity model with reaction-time delay of drivers. The stability condition of this model is obtained by using the linear stability theory. The results show that the decrease of reaction-time delay of drivers leads to the stabilization of traffic flow. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the density waves in the stable, metastable and unstable regions respectively. The triangular shock waves, soliton waves and kink–antikink waves appearing respectively in the three distinct regions are derived to describe the traffic jams. The numerical simulations are given.

Suggested Citation

  • Yu, Lei & Li, Tong & Shi, Zhong-Ke, 2010. "Density waves in a traffic flow model with reaction-time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(13), pages 2607-2616.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:13:p:2607-2616
    DOI: 10.1016/j.physa.2010.03.009
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    Citations

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    Cited by:

    1. Xin, Qi & Yang, Nan & Fu, Rui & Yu, Shaowei & Shi, Zhongke, 2018. "Impacts analysis of car following models considering variable vehicular gap policies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 501(C), pages 338-355.
    2. Zheng, Liang & Jin, Peter J. & Huang, Helai, 2015. "An anisotropic continuum model considering bi-directional information impact," Transportation Research Part B: Methodological, Elsevier, vol. 75(C), pages 36-57.
    3. Zhang, Yu & Wang, Sha & Pan, Dong-bo & Zhang, Geng, 2021. "Stability analysis for a new lattice hydrodynamic model with time-varying delay in sensing traffic flux," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    4. Qin, Shunda & He, Zhiting & Cheng, Rongjun, 2018. "An extended lattice hydrodynamic model based on control theory considering the memory effect of flux difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 809-816.
    5. Junyan Han & Xiaoyuan Wang & Gang Wang, 2022. "Modeling the Car-Following Behavior with Consideration of Driver, Vehicle, and Environment Factors: A Historical Review," Sustainability, MDPI, vol. 14(13), pages 1-27, July.
    6. Changtao-Jiang, & Rongjun-Cheng, & Hongxia-Ge,, 2019. "Mean-field flow difference model with consideration of on-ramp and off-ramp," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 465-476.
    7. Jiang, Changtao & Cheng, Rongjun & Ge, Hongxia, 2018. "Effects of speed deviation and density difference in traffic lattice hydrodynamic model with interruption," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 900-908.
    8. Mei, Yiru & Zhao, Xiaoqun & Qian, Yeqing & Xu, Shangzhi & Li, Zhipeng, 2021. "Research on the influence of multiple historical speed information with different weight distribution on traffic flow stability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 563(C).

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