考虑延迟效应的交通流宏观流体力学模型

Macroscopic Hydrodynamic Model of Traffic Flow Considering Delay Effect

关键词:  优化速度模型  宏观转化  流体力学模型  连续性方程  KdV-Burgers方程  延迟效应

Key words:  optimal velocity model  macroscopic transformation  hydrodynamic model  continuum equation  KdV-Burgers equation  delay effect

摘要:

[目的]研究延迟效应的高阶宏观流体力学模型及其对交通流密度波产生的影响。[方法]通过宏观转化法将微观量转换成宏观量,推导出关于延迟效应的高阶动力学模型。同时结合交通流的守恒连续性方程,对新的动力学模型进行线性分析和非线性分析。用迎风格式数值模拟研究在不同延迟时间和密度下的交通流的成簇效应和系统的稳定性。[结果]推导出的模型具有各向异性的特性。在线性稳定性分析和非线性分析中分别推导出在微扰的条件下交通流的稳定性条件和描述密度波的KdV-Burgers方程,并求得密度波解。数值模拟结果表明考虑了延迟效应的模型系统不稳定状态范围在缩小。[结论]考虑了延迟效应的宏观流体力学模型,交通流成簇效应减弱。这表明交通流的拥堵得到抑制,有利于系统稳定。

Abstract:

[Objective] This paper studies the high-order macroscopic hydrodynamic model with delay effect and the effect of density wave in traffic flow.[Methods] Using the relation of transformation from microscopic model to macroscopic one, the high-order hydrodynamic traffic model is derived. By the stability analysis and nonlinear analysis, the stability condition of the high-order hydrodynamic traffic model is obtained and KdV-Burgers equation to depict density-wave is derived.Using the upwind scheme performs the simulation to study the clustering effect and the system's stability for different delay time and density.[Results] The derived model is of the property of anisotropy.The stability condition is obtained under the action of a small perturbation and KdV-Burgers equation to depict density-wave between metastable state and free flow is derived by nonlinear analysis. Numerical simulation results indicate that the range of system's unstable state was decreased under considering the delay effect model.[Conclusion] It is found that the macroscopic hydrodynamic model derived from considering the delay effect can theoretically and numerically decline clustering effect in traffic flow under the one-dimensional periodic boundary condition. Results indicate that the traffic congestion is better suppressed and the delay effect is conducive to the stability of traffic system.