TDGL and MKdV equations for jamming transition in the lattice models of traffic
TDGL and MKdV equations for jamming transition in the lattice models of traffic
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DOI：
10.1016/s0378-4371(98)00466-x
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发表时间：
1999-03
影响因子：
3.3
通讯作者：
T. Nagatani
中科院分区：
文献类型：
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作者：
T. Nagatani
利用相变和临界现象的热力学术语，建立了描述高速公路交通流堵塞转变的格点模型。它们是交通流体动力学模型的格子版本。本文提出了两种格点模型：一种是时间为连续变量、空间为离散变量的微分-差分方程，另一种是时间和空间均为离散变量的差分方程。我们将线性稳定性理论和非线性分析应用于格点模型。结果表明，时间相关的金-朗道（TDGL）方程推导出描述交通流的临界点附近。建立了描述相变和临界现象的热力学理论。推导了描述交通阻塞的扰动修正Korteweg-de弗里斯（MKdV）方程。
The lattice models of traffic are proposed to describe the jamming transition in traffic flow on a highway in terms of thermodynamic terminology of phase transitions and critical phenomena. They are the lattice versions of the hydrodynamic model of traffic. Two lattice models are presented: one is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other is the difference equation in which both time and space variables are discrete. We apply the linear stability theory and the nonlinear analysis to the lattice models. It is shown that the time-dependent Ginzburg–Landau (TDGL) equation is derived to describe the traffic flow near the critical point. A thermodynamic theory is formulated for describing the phase transitions and critical phenomena. It is also shown that the perturbed modified Korteweg-de Vries (MKdV) equation is derived to describe the traffic jam.