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Friction coefficient and radius of curvature effects upon traffic flow on a curved Road

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  • Zhu, Wen-Xing
  • Zhang, Li-Dong

Abstract

We investigate the friction coefficient and radius of curvature effects upon traffic flow analytically and numerically. A new model is proposed to describe the motion of vehicles running on a curved road. The stability condition is obtained by the use of control theories. The nonlinear analysis method is taken to derive the modified KdV (Korteweg–de Vries) equation and the kink–antikink solution is obtained near the critical point. Simulations are carried out to verify the double effects upon traffic flow. The flux increases but the stability decreases with an increase of the two parameters. Numerical results are in good agreement with the analytical results.

Suggested Citation

  • Zhu, Wen-Xing & Zhang, Li-Dong, 2012. "Friction coefficient and radius of curvature effects upon traffic flow on a curved Road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4597-4605.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:20:p:4597-4605
    DOI: 10.1016/j.physa.2012.05.032
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    Citations

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    Cited by:

    1. Liu, Fangxun & Cheng, Rongjun & Ge, Hongxia & Yu, Chenyan, 2016. "A new car-following model with consideration of the velocity difference between the current speed and the historical speed of the leading car," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 464(C), pages 267-277.
    2. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2018. "An extended car-following model under V2V communication environment and its delayed-feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 508(C), pages 349-358.
    3. Jiang, Nan & Yu, Bin & Cao, Feng & Dang, Pengfei & Cui, Shaohua, 2021. "An extended visual angle car-following model considering the vehicle types in the adjacent lane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    4. Kaur, Ramanpreet & Sharma, Sapna, 2018. "Modeling and simulation of driver’s anticipation effect in a two lane system on curved road with slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 499(C), pages 110-120.
    5. Shuang Jin & Jianxi Yang & Zhongcheng Liu, 2022. "Modeling and Analysis of Car-Following for Intelligent Connected Vehicles Considering Expected Speed in Helical Ramps," Sustainability, MDPI, vol. 14(24), pages 1-20, December.
    6. Hou, Qinzhong & Meng, Xianghai & Leng, Junqiang & Yu, Lu, 2018. "Application of a random effects negative binomial model to examine crash frequency for freeways in China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 937-944.
    7. 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.
    8. Hou, Qinzhong & Meng, Xianghai & Huo, Xiaoyan & Cheng, Yuxing & Leng, Junqiang, 2019. "Effects of freeway climbing lane on crash frequency: Application of propensity scores and potential outcomes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 517(C), pages 246-256.
    9. Junyan Han & Xiaoyuan Wang & Gang Wang, 2022. "Modeling the Car-Following Behavior with Consideration of Driver, Vehicle, and Environment Factors: A Historical Review," Sustainability, MDPI, vol. 14(13), pages 1-27, July.
    10. Leng, Jun-Qiang & Zhao, Lin, 2017. "Analysis of electric vehicle’s trip cost without late arrival," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 469(C), pages 761-766.
    11. Leng, Jun-Qiang & Liu, Wei-Yi & Zhao, Lin, 2017. "Analysis of electric vehicle’s trip cost allowing late arrival," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 473(C), pages 293-300.
    12. Zhang, Futao & Qian, Yongsheng & Zeng, Junwei & Xu, Dejie & Li, Haijun, 2023. "Stability and safety analysis of mixed traffic flow considering network function degradation and platoon driving on the road with a slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 630(C).

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