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A Dynamical Model With Next-Nearest-Neighbor Interaction In Relative Velocity

Author

Listed:
  • ZHIPENG LI

    (School of Electronics and Information Engineering, Tongji University, Shanghai, 200092, China)

  • YUNCAI LIU

    (Institute of Image Processing and Pattern Recognition, Shanghai Jiao Tong University, Shanghai, 200240, China)

  • FUQIANG LIU

    (School of Electronics and Information Engineering, Tongji University, Shanghai 200092, China)

Abstract

By introducing the velocity difference between the preceding car and the car before the preceding one into the optimal velocity model (OVM), we present an extended dynamical model which takes into account the next-nearest-neighbor interaction in relative velocity. The stability condition of this model is derived by considering a small perturbation around the uniform flow solution and the validity of our theoretical analysis is also confirmed by direct simulations. The analytic and simulation results indicate that traffic congestion is suppressed efficiently by incorporating the effect of new consideration. Moreover, the effect of the new consideration is investigated by numerical simulation. In particular, the jamming flow, the current-density relation, and the propagation speed of small disturbance are examined in detail by varying various values of the parameter.

Suggested Citation

  • Zhipeng Li & Yuncai Liu & Fuqiang Liu, 2007. "A Dynamical Model With Next-Nearest-Neighbor Interaction In Relative Velocity," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 819-832.
    • Handle: RePEc:wsi:ijmpcx:v:18:y:2007:i:05:n:s0129183107010450
    DOI: 10.1142/S0129183107010450
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    Cited by:

    1. Wang, Zihao & Ge, Hongxia & Cheng, Rongjun, 2020. "An extended macro model accounting for the driver’s timid and aggressive attributions and bounded rationality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    2. Liu, Huaqing & Zheng, Pengjun & Zhu, Keqiang & Ge, Hongxia, 2015. "KdV–Burgers equation in the modified continuum model considering anticipation effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 438(C), pages 26-31.
    3. Chen, Can & Cheng, Rongjun & Ge, Hongxia, 2019. "An extended car-following model considering driver’s sensory memory and the backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 278-289.

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