Density waves in traffic flow
Density waves in traffic flow
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DOI：
10.1103/physreve.61.3564
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发表时间：
2000-04-01
影响因子：
2.4
通讯作者：
Nagatani, T
中科院分区：
文献类型：
--
作者：
Nagatani, T
对车辆跟驰模型中的密度波进行了解析和数值研究。这项工作是我们之前对亚稳定和不稳定区域交通流研究的延续[Phys. Rev. E 58，5471（1998）; 60，180（1999）]。本文用非线性分析方法导出了交通流稳定区密度波的Burgers方程。数值计算表明，在稳定区的后期，三角形激波以密度波的形式出现。计算了冲击波的衰减率，并与解析结果进行了比较。结果表明，在共存曲线外、在旋节线附近和旋节线内的密度波分别以三角形激波、孤立子和扭结-反扭结波的形式出现。密度波分别用Burgers方程、Korteweg-de弗里斯方程和修正的Korteweg-de弗里斯方程描述。
Density waves are investigated in the car-following model analytically and numerically. This work is a continuation of our previous investigation of traffic flow in the metastable and unstable regions [Phys. Rev. E 58, 5471 (1998); 60, 180 (1999)]. The Burgers equation is derived for the density wave in the stable region of traffic flow by the use of nonlinear analysis. It is shown, numerically, that the triangular shock wave appears as the density wave at the late stage in the stable region. The decay rate of the shock wave is calculated and compared with the analytical result. It is shown that the density waves out of the coexisting curve, near the spinodal line, and within the spinodal line appear, respectively, as the triangular shock wave, the soliton, and the kink-antikink wave. The density waves are described, respectively, by the Burgers, Korteweg-de Vries, and modified Korteweg-de Vries equations.