Jamming transitions and the modified Korteweg–de Vries equation in a two-lane traffic flow
Jamming transitions and the modified Korteweg–de Vries equation in a two-lane traffic flow
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DOI：
10.1016/s0378-4371(98)00563-9
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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：
--
作者：
T. Nagatani
提出了两个点阵模型来模拟双车道高速公路上的交通流。它们是交通流体动力学模型的格子版本：一个（模型 A）由微分方程描述，其中时间是连续变量，空间是离散变量；另一个（模型 B）是时间和空间变量都是离散变量的差分方程。利用非线性分析和计算机仿真研究了自由运动阶段、共存阶段和均匀拥塞阶段之间的干扰转变。修正的 Korteweg–de Vries (MKdV) 方程是从临界点附近的晶格模型导出的。交通堵塞通过从 MKdV 方程获得的扭结-反扭结解来描述。研究发现，临界点、共存曲线和中性稳定线随着换道率的增加而减小。同时对模型B进行了计算机仿真，结果表明，由MKdV方程得到的共存曲线与仿真结果一致。
The two lattice models are presented to simulate the traffic flow on a two-lane highway. They are the lattice versions of the hydrodynamic model of traffic: the one (model A) is described by the differential-difference equation where time is a continuous variable and space is a discrete variable, and the other (model B) is the difference equation in which both time and space variables are discrete. The jamming transitions among the freely moving phase, the coexisting phase, and the uniform congested phase are studied by using the nonlinear analysis and the computer simulation. The modified Korteweg–de Vries (MKdV) equations are derived from the lattice models near the critical point. The traffic jam is described by a kink–antikink solution obtained from the MKdV equation. It is found that the critical point, the coexisting curve, and the neutral stability line decrease with increasing the rate of lane changing. Also, the computer simulation is performed for the model B. It is shown that the coexisting curves obtained from the MKdV equation are consistent with the simulation result.