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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

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