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Nonlinear analysis of traffic flow on a gradient highway

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  • Zhu, Wen-Xing
  • Yu, Rui-Ling

Abstract

We investigate the slope effects upon traffic flow on a single lane gradient (uphill/downhill) highway analytically and numerically. The stability condition, neutral stability condition and instability condition are obtained by the use of linear stability theory. It is found that stability of traffic flow on the gradient varies with the slopes. The Burgers, Korteweg–de Vries (KdV) and modified Korteweg–de Vries (mKdV) equations are derived to describe the triangular shock waves, soliton waves and kink–antikink waves in the stable, meta-stable and unstable region respectively. A series of simulations are carried out to reproduce the triangular shock waves, kink–antikink waves and soliton waves. Results show that amplitudes of the triangular shock waves and kink–antikink waves vary with the slopes, the soliton wave appears in an upward form when the average headway is less than the safety distance and a downward form when the average headway is more than the safety distance. Moreover both the kink–antikink waves and the solitary waves propagate backwards. The numerical simulation shows a good agreement with the analytical result.

Suggested Citation

  • Zhu, Wen-Xing & Yu, Rui-Ling, 2012. "Nonlinear analysis of traffic flow on a gradient highway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 954-965.
    • Handle: RePEc:eee:phsmap:v:391:y:2012:i:4:p:954-965
    DOI: 10.1016/j.physa.2011.09.026
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    Citations

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    Cited by:

    1. Huimin Liu & Rongjun Cheng & Tingliu Xu, 2021. "Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect," Mathematics, MDPI, vol. 9(19), pages 1-13, October.
    2. Zhao, Jing & Li, Peng, 2016. "An extended car-following model with consideration of speed guidance at intersections," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 1-8.
    3. Yin, Jiacheng & Li, Zongping & Cao, Peng & Li, Linheng & Ju, Yanni, 2023. "Car-following modeling based on Morse model with consideration of road slope in connected vehicles environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    4. Zhai, Cong & Wu, Weitiao, 2022. "A continuum model considering the uncertain velocity of preceding vehicles on gradient highways," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 588(C).
    5. 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.
    6. 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).
    7. Peng, Guanghan & Li, Xinhai & Wang, Hailing & Tan, Huili, 2024. "Bifurcation and phase transitions in car-following model integrating driver's characteristic and speed limit on spiral slope roads," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    8. 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.
    9. 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.
    10. Li, Yongfu & Zhao, Hang & Zhang, Li & Zhang, Chao, 2018. "An extended car-following model incorporating the effects of lateral gap and gradient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 177-189.
    11. 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.
    12. Wang, Zihao & Zhu, Wen-Xing, 2022. "Modeling and stability analysis of traffic flow considering electronic throttle dynamics on a curved road with slope," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    13. 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.
    14. Sun, Yuqing & Ge, Hongxia & Cheng, Rongjun, 2019. "A car-following model considering the effect of electronic throttle opening angle over the curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).

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