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Nonlinear analysis of an extended traffic flow model in ITS environment

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  • Yu, Lei
  • Shi, Zhongke

Abstract

An extended traffic flow model is proposed by introducing the relative velocity of arbitrary number of cars that precede and that follow into the Newell–Whitham-type car-following model. The stability condition of this model is obtained by using the linear stability theory. The results show that the stability of traffic flow is improved by taking into account the relative velocity of cars ahead and backward. By applying the nonlinear analysis the modified Korteweg-de Vries (mKdV) equation is derived to describe the traffic behavior near the critical point. The kink–antikink soliton, the solution of the mKdV equation, is obtained to describe the traffic jams. From the numerical simulation, it is shown that the traffic jams are suppressed efficiently by taking into account the relative velocity of cars ahead and backward. The analytical results are consistent with the simulation one.

Suggested Citation

  • Yu, Lei & Shi, Zhongke, 2008. "Nonlinear analysis of an extended traffic flow model in ITS environment," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 550-558.
    • Handle: RePEc:eee:chsofr:v:36:y:2008:i:3:p:550-558
    DOI: 10.1016/j.chaos.2007.07.076
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    Cited by:

    1. 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).
    2. Hu, Junjie & Hu, Cheng & Yang, Jiayu & Bai, Jun & Lee, Jaeyoung Jay, 2024. "Do traffic flow states follow Markov properties? A high-order spatiotemporal traffic state reconstruction approach for traffic prediction and imputation," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).
    3. Ai, Wen-Huan & Shi, Zhong-Ke & Liu, Da-Wei, 2015. "Bifurcation analysis of a speed gradient continuum traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 418-429.
    4. Zhang, Jing & Xu, Keyu & Li, Guangyao & Li, Shubin & Wang, Tao, 2021. "Dynamics of traffic flow affected by the future motion of multiple preceding vehicles under vehicle-connected environment: Modeling and stabilization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 565(C).
    5. S. I. Oni & Charles Asenime, 2008. "A Daily Flow Profile of Traffic in an Urban Traffic Corridor: The Nigerian Experience," Indus Journal of Management & Social Science (IJMSS), Department of Business Administration, vol. 2(2), pages 99-109, December.
    6. Zhai, Cong & Li, Kening & Zhang, Ronghui & Peng, Tao & Zong, Changfu, 2024. "Phase diagram in multi-phase heterogeneous traffic flow model integrating the perceptual range difference under human-driven and connected vehicles environment," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

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