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A continuum model considering the uncertain velocity of preceding vehicles on gradient highways

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  • Zhai, Cong
  • Wu, Weitiao

Abstract

Gradient roads are not uncommon in mountainous areas and freeways. The driving field of vision will be limited under such a complex road environment, which hinders the drivers from accurately perceiving the speed of the preceding vehicle. Accurate modeling of traffic flow in such an environment is therefore paramount to make accurate predictions and to effectively control the system. To this end, we present a modified continuum model accounting for the uncertain velocity of preceding vehicles on gradient highways. We derive the stability criterion and the KdV–Burgers equation of the proposed model via linear and nonlinear stability analysis. The density wave solution obtained by solving the above KdV–Burgers equation can explain the propagation mechanism of traffic jams near the stability curve. Numerical examples reveal that the slope information and uncertainty term exert great influence on traffic jams and energy consumption. Specifically, the effect of the slope information is positive, whereas the effect of the uncertainty term is negative.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:phsmap:v:588:y:2022:i:c:s0378437121008347
    DOI: 10.1016/j.physa.2021.126561
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    References listed on IDEAS

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    Cited by:

    1. Zhai, Cong & Zhang, Ronghui & Peng, Tao & Zhong, Changfu & Xu, Hongguo, 2023. "Heterogeneous lattice hydrodynamic model and jamming transition mixed with connected vehicles and human-driven vehicles," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 623(C).
    2. Zhai, Cong & Wu, Weitiao & Xiao, Yingping & Luo, Qiang & Zhang, Yusong, 2022. "Modeling bidirectional pedestrian flow with the perceived uncertainty of preceding pedestrian information," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    3. Peng, Guanghan & Xu, Mingzuo & Tan, Huili, 2024. "Phase transition in a new heterogeneous macro continuum model of traffic flow under rain and snow weather environment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 637(C).
    4. 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.
    5. Zhai, Cong & Wu, Weitiao & Xiao, Yingping, 2023. "The jamming transition of multi-lane lattice hydrodynamic model with passing effect," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    6. Ma, Guangyi & Li, Keping, 2024. "Analysis and simulation of vehicle following behavior with consideration of multiple time delays," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 634(C).

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