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Nonlinear analysis of the optimal velocity difference model with reaction-time delay

Author

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  • Zhou, Jie
  • Shi, Zhong-Ke
  • Cao, Jin-Liang

Abstract

We investigate the effect of reaction-time delay of drivers upon traffic flow analytically and numerically. We extend the optimal velocity difference model by taking reaction-time delay of drivers into account. The stability condition is obtained. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived in the stable, metastable and unstable regions. The results show that the increase of reaction-time delay of drivers leads to the unrealistic traffic phenomena and unstable traffic flow. By adjusting the coefficient of the velocity and optimal velocity difference, the unrealistic traffic phenomena and unstable traffic flow can disappear.

Suggested Citation

  • Zhou, Jie & Shi, Zhong-Ke & Cao, Jin-Liang, 2014. "Nonlinear analysis of the optimal velocity difference model with reaction-time delay," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 396(C), pages 77-87.
    • Handle: RePEc:eee:phsmap:v:396:y:2014:i:c:p:77-87
    DOI: 10.1016/j.physa.2013.11.007
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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. Hossain, Md. Anowar & Tanimoto, Jun, 2022. "A microscopic traffic flow model for sharing information from a vehicle to vehicle by considering system time delay effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 585(C).
    3. 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.
    4. Zhou, Tong & Chen, Dong & Zheng, Linjiang & Liu, Weining & He, Yuchu & Liu, Zhongcheng, 2018. "Feedback-based control for coupled map car-following model with time delays on basis of linear discrete-time system," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 512(C), pages 174-185.
    5. Wang, Pengcheng & Yu, Guizhen & Wu, Xinkai & Qin, Hongmao & Wang, Yunpeng, 2018. "An extended car-following model to describe connected traffic dynamics under cyberattacks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 351-370.

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