Analysis of the stability and density waves for traffic flow
Analysis of the stability and density waves for traffic flow
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DOI：
10.1088/1009-1963/11/11/007
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发表时间：
2005-06
期刊：
影响因子：
--
通讯作者：
薛郁
中科院分区：
文献类型：
--
作者：
薛郁
本文将交通最优速度模型扩展为考虑相对速度的模型。用摄动法分析了交通流的稳定性波和密度波。通过线性稳定性分析，导出了稳定性判据。结果表明，三角激波、孤子波和扭结波分别出现在三个区域的密度波模型中；稳定、亚稳和不稳定区域。这些对应于Burgers方程、Korteweg-de Vries方程和修正Korteweg-de Vires方程的解。分析结果与数值模拟结果吻合较好。结果表明，车辆与相对速度的相互作用会影响交通流的稳定性，提高临界密度。
In this paper,the optimal velocity model of traffic is extended to take into account the relative velocity.The stability and density waves for traffic flow are investigated analytically with the perturbation method.The stability criterion is dervied by the linear stability analysis.It is shown that the triangular shock wave,soliton wave and kink wave appear respectivley in our model for density waves in the three regions;stable,metastable and unstable regions.Theses Correspond to the solutions of the Burgers equation,Korteweg-de Vries equation and modified Korteweg-de Vires equation.The analytical resulsts are confirmed to be in good agreement with those of numerical simulation.All the results indicate that the interaction of a car with relative velocity can affect the stability of the traffic flow and raise critical density.