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Numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries

Author

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  • Zhu, H.B.
  • Dai, S.Q.

Abstract

The soliton and kink–antikink density waves are simulated with periodic boundaries, by adding perturbation in the initial condition on single-lane road based on a car-following model. They are reproduced in the form of the space–time evolution of headway, both of which propagate backwards. It is found that the solitons appear only near the neutral stability line regardless of the boundary conditions, and they exhibit upward form when the initial headway is smaller than the safety distance, otherwise they exhibit downward form. Comparison is made between the numerical and analytical results about the amplitude of kink–antikink wave, and the underlying mechanism is analyzed. Besides, it is indicated that the maximal current of traffic flow increases with decreasing safety distance. The numerical simulation shows a good agreement with the analytical results.

Suggested Citation

  • Zhu, H.B. & Dai, S.Q., 2008. "Numerical simulation of soliton and kink density waves in traffic flow with periodic boundaries," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(16), pages 4367-4375.
    • Handle: RePEc:eee:phsmap:v:387:y:2008:i:16:p:4367-4375
    DOI: 10.1016/j.physa.2008.01.067
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    Citations

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    Cited by:

    1. Rongjun, Cheng & Hongxia, Ge & Jufeng, Wang, 2018. "The nonlinear analysis for a new continuum model considering anticipation and traffic jerk effect," Applied Mathematics and Computation, Elsevier, vol. 332(C), pages 493-505.
    2. 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.
    3. 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.
    4. Cheng, Rongjun & Ge, Hongxia & Sun, Fengxin & Wang, Jufeng, 2018. "An extended macro model accounting for acceleration changes with memory and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 270-283.
    5. Qingtao, Zhai & Hongxia, Ge & Rongjun, Cheng, 2018. "An extended continuum model considering optimal velocity change with memory and numerical tests," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 490(C), pages 774-785.

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