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Analysis of a Novel Two-Dimensional Lattice Hydrodynamic Model Considering Predictive Effect

Author

Listed:
  • Huimin Liu

    (Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China)

  • Rongjun Cheng

    (Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China)

  • Tingliu Xu

    (Faculty of Maritime and Transportation, Ningbo University, Ningbo 315211, China
    Merchant Marine College, Shanghai Maritime University, Shanghai 201306, China)

Abstract

In actual driving, the driver can estimate the traffic condition ahead at the next moment in terms of the current traffic information, which describes the driver’s predictive effect. Due to this factor, a novel two-dimensional lattice hydrodynamic model considering a driver’s predictive effect is proposed in this paper. The stability condition of the novel model is obtained by performing the linear stability analysis method, and the phase diagram between the driver’s sensitivity coefficient and traffic density is drawn. The nonlinear analysis of the model is conducted and the kink-antikink of modified Korteweg-de Vries (mKdV) equation is derived, which describes the propagation characteristics of the traffic density flow waves near the critical point. The numerical simulation is executed to explore how the driver’s predictive effect affects the traffic flow stability. Numerical results coincide well with theoretical analysis results, which indicates that the predictive effect of drivers can effectively avoid traffic congestion and the fraction of eastbound cars can also improve the stability of traffic flow to a certain extent.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:19:p:2464-:d:649223
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    References listed on IDEAS

    as
    1. Zhang, Jing & Xu, Keyu & Li, Shubin & Wang, Tao, 2020. "A new two-lane lattice hydrodynamic model with the introduction of driver’s predictive effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    2. Zhao, Hongzhuan & Xia, Dongxue & Yang, Shuhong & Peng, Guanghan, 2020. "The delayed-time effect of traffic flux on traffic stability for two-lane freeway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    3. An, Shuke & Xu, Liangjie & Qian, Lianghui & Chen, Guojun & Luo, Haoshun & Li, Fu, 2020. "Car-following model for autonomous vehicles and mixed traffic flow analysis based on discrete following interval," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 560(C).
    4. Wang, Tao & Zang, Rudong & Xu, Keyu & Zhang, Jing, 2019. "Analysis of predictive effect on lattice hydrodynamic traffic flow model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    5. Peng, Guanghan & Kuang, Hua & Qing, Li, 2018. "A new lattice model of traffic flow considering driver’s anticipation effect of the traffic interruption probability," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 374-380.
    6. Wang, Jufeng & Sun, Fengxin & Ge, Hongxia, 2019. "An improved lattice hydrodynamic model considering the driver’s desire of driving smoothly," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 119-129.
    7. Zhu, Wen-Xing & Zhang, H.M., 2018. "Analysis of mixed traffic flow with human-driving and autonomous cars based on car-following model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 496(C), pages 274-285.
    8. Cheng, Rongjun & Wang, Yunong, 2019. "An extended lattice hydrodynamic model considering the delayed feedback control on a curved road," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 513(C), pages 510-517.
    9. Wu, Xia & Zhao, Xiangmo & Song, Huansheng & Xin, Qi & Yu, Shaowei, 2019. "Effects of the prevision relative velocity on traffic dynamics in the ACC strategy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 192-198.
    10. Nagatani, Takashi, 1998. "Modified KdV equation for jamming transition in the continuum models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 599-607.
    11. Chang, Yinyin & He, Zhiting & Cheng, Rongjun, 2019. "An extended lattice hydrodynamic model considering the driver’s sensory memory and delayed-feedback control," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 514(C), pages 522-532.
    12. Ou, Hui & Tang, Tie-Qiao, 2018. "An extended two-lane car-following model accounting for inter-vehicle communication," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 495(C), pages 260-268.
    13. Li, Lixiang & Cheng, Rongjun & Ge, Hongxia, 2021. "New feedback control for a novel two-dimensional lattice hydrodynamic model considering driver’s memory effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 561(C).
    14. Nagatani, Takashi, 1999. "TDGL and MKdV equations for jamming transition in the lattice models of traffic," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 264(3), pages 581-592.
    15. 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.
    16. Peng, G.H. & Song, W. & Peng, Y.J. & Wang, S.H., 2014. "A novel macro model of traffic flow with the consideration of anticipation optimal velocity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 76-82.
    17. Peng, Guanghan & Zhao, Hongzhuan & Li, Xiaoqin, 2019. "The impact of self-stabilization on traffic stability considering the current lattice’s historic flux for two-lane freeway," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 31-37.
    18. Daljeet Kaur & Sapna Sharma, 2020. "The impact of the predictive effect on traffic dynamics in a lattice model with passing," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 93(3), pages 1-10, March.
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