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Linear stability and nonlinear analyses of traffic waves for the general nonlinear car-following model with multi-time delays

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  • Sun, Dihua
  • Chen, Dong
  • Zhao, Min
  • Liu, Weining
  • Zheng, Linjiang

Abstract

In this paper, the general nonlinear car-following model with multi-time delays is investigated in order to describe the reactions of vehicle to driving behavior. Platoon stability and string stability criteria are obtained for the general nonlinear car-following model. Burgers equation and Korteweg de Vries (KdV) equation and their solitary wave solutions are derived adopting the reductive perturbation method. We investigate the properties of typical optimal velocity model using both analytic and numerical methods, which estimates the impact of delays about the evolution of traffic congestion. The numerical results show that time delays in sensing relative movement is more sensitive to the stability of traffic flow than time delays in sensing host motion.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:501:y:2018:i:c:p:293-307
    DOI: 10.1016/j.physa.2018.02.179
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    References listed on IDEAS

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    1. Jia, Dongyao & Ngoduy, Dong, 2016. "Enhanced cooperative car-following traffic model with the combination of V2V and V2I communication," Transportation Research Part B: Methodological, Elsevier, vol. 90(C), pages 172-191.
    2. Treiber, Martin & Kesting, Arne & Helbing, Dirk, 2006. "Delays, inaccuracies and anticipation in microscopic traffic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 71-88.
    3. 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.
    4. 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.
    5. Tang, Tie-Qiao & Chen, Liang & Huang, Hai-Jun & Song, Ziqi, 2016. "Analysis of the equilibrium trip cost without late arrival and the corresponding traffic properties using a car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 460(C), pages 348-360.
    6. Yu, Shaowei & Zhao, Xiangmo & Xu, Zhigang & Shi, Zhongke, 2016. "An improved car-following model considering the immediately ahead car’s velocity difference," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 446-455.
    7. G. F. Newell, 1961. "Nonlinear Effects in the Dynamics of Car Following," Operations Research, INFORMS, vol. 9(2), pages 209-229, April.
    8. Yu, Shaowei & Huang, Mengxing & Ren, Jia & Shi, Zhongke, 2016. "An improved car-following model considering velocity fluctuation of the immediately ahead car," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 449(C), pages 1-17.
    9. Davis, L.C., 2003. "Modifications of the optimal velocity traffic model to include delay due to driver reaction time," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 319(C), pages 557-567.
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    Cited by:

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    2. Chen, Dong & Zhao, Min & Sun, Dihua & Zheng, Linjiang & Jin, Shuang & Chen, Jin, 2020. "Robust H∞ control of cooperative driving system with external disturbances and communication delays in the vicinity of traffic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 542(C).
    3. 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.
    4. He, Z.C. & Kang, H. & Li, Eric & Zhou, E.L. & Cheng, H.T. & Huang, Y.Y., 2022. "Coordinated control of heterogeneous vehicle platoon stability and energy-saving control strategies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    5. 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).
    6. Wang, Xiaoning & Liu, Minzhuang & Ci, Yusheng & Wu, Lina, 2022. "Effect of front two adjacent vehicles’ velocity information on car-following model construction and stability analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 607(C).
    7. Yifan Pan & Yongjiang Wang & Baobin Miao & Rongjun Cheng, 2022. "Stabilization Strategy of a Novel Car-Following Model with Time Delay and Memory Effect of the Driver," Sustainability, MDPI, vol. 14(12), pages 1-20, June.

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