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Theoretical analysis of the density wave in a new continuum model and numerical simulation

Author

Listed:
  • Lai, Ling-Ling
  • Cheng, Rong-Jun
  • Li, Zhi-Peng
  • Ge, Hong-Xia

Abstract

Considered the effect of traffic anticipation in the real world, a new anticipation driving car following model (AD-CF) was proposed by Zheng et al. Based on AD-CF model, adopted an asymptotic approximation between the headway and density, a new continuum model is presented in this paper. The neutral stability condition is obtained by applying the linear stability theory. Additionally, the Korteweg–de Vries (KdV) equation is derived via nonlinear analysis to describe the propagating behavior of traffic density wave near the neutral stability line. The numerical simulation and the analytical results show that the new continuum model is capable of explaining some particular traffic phenomena.

Suggested Citation

  • Lai, Ling-Ling & Cheng, Rong-Jun & Li, Zhi-Peng & Ge, Hong-Xia, 2014. "Theoretical analysis of the density wave in a new continuum model and numerical simulation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 283-290.
    • Handle: RePEc:eee:phsmap:v:402:y:2014:i:c:p:283-290
    DOI: 10.1016/j.physa.2014.01.026
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    Citations

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    Cited by:

    1. Tang, Tie-Qiao & Zhang, Jian & Liu, Kai, 2017. "A speed guidance model accounting for the driver’s bounded rationality at a signalized intersection," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 45-52.
    2. Wang, Zihao & Ge, Hongxia & Cheng, Rongjun, 2018. "Nonlinear analysis for a modified continuum model considering driver’s memory and backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 18-27.
    3. Liu, Zhaoze & Ge, Hongxia & Cheng, Rongjun, 2018. "KdV–Burgers equation in the modified continuum model considering the effect of friction and radius on a curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 1218-1227.
    4. Jiao, Yulei & Ge, Hongxia & Cheng, Rongjun, 2019. "Nonlinear analysis for a modified continuum model considering electronic throttle (ET) and backward looking effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    5. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of social optimum for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 275-283.
    6. Li, Chuan-Yao & Huang, Hai-Jun & Tang, Tie-Qiao, 2017. "Analysis of user equilibrium for staggered shifts in a single-entry traffic corridor with no late arrivals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 8-18.
    7. Zhaoze, Liu & Rongjun, Cheng & Hongxia, Ge, 2019. "Research on preceding vehicle’s taillight effect and energy consumption in an extended macro traffic model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 525(C), pages 304-314.
    8. Li, Chuan-Yao & Xu, Guang-Ming & Tang, Tie-Qiao, 2018. "Social optimum for evening commute in a single-entry traffic corridor with no early departures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 236-247.

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