A NON-EQUILIBRIUM TRAFFIC MODEL DEVOID OF GAS-LIKE BEHAVIOR
A NON-EQUILIBRIUM TRAFFIC MODEL DEVOID OF GAS-LIKE BEHAVIOR
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DOI：
10.1016/s0191-2615(00)00050-3
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发表时间：
2002-03
影响因子：
6.8
通讯作者：
H. M. Zhang
中科院分区：
文献类型：
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作者：
H. M. Zhang
现有的高阶连续统模型的有效性在最近的文献中受到了严重的挑战。对这些模型的主要反对意见是，它们表现出类似气体的行为，也就是说，它们预测后面的车辆可以影响前面车辆的行为，如Daganzo [Transp. B 29（1995）277]。致力于消除这种缺陷的相当大的努力（del Castillo等人[In：C. F. Daganzo（Ed.），运输和交通理论，爱思唯尔科学，阿姆斯特丹，1993，第387页]，张[Transp. Res. B 32（7）（1998）485; Transp. Res. B 33（6）（1999）387; Transp. B 34（2000）583]）只取得了部分成功。在本文中，我们提出了一个非平衡交通模型，是没有像气体的行为，困扰其他高阶模型。描述该模型的偏微分方程组是双曲型的，并且具有两个特征场：一个是真正的非线性场，另一个是线性退化的。第一个场产生类似于Lighthill-Whitham-理查兹（LWR）模型的激波和稀疏波，而第二个场产生接触不连续。所有这些波的传播速度不超过交通速度，因此车辆的轨迹不会受到后面发生的事情的影响。该模型还显示出正确的末端行为，并能够解释一些观察到的挑战旧模型的交通现象。
The validity of existing higher-order continuum models has been seriously challenged in recent literature. A primary objection to these models is that they exhibit gas-like behavior, that is, they predict that vehicles from behind can influence the behavior of vehicles in front, as elucidated by Daganzo [Transp. Res. B 29 (1995) 277]. Considerable efforts devoted to remove this deficiency (del Castillo et al. [In: C.-F. Daganzo (Ed.), Transportation and Traffic Theory, Elsevier Science, Amsterdam, 1993, p. 387], Zhang [Transp. Res. B 32(7) (1998) 485; Transp. Res. B 33(6) (1999) 387; Transp. Res. B 34 (2000) 583]) have met with only partial success. In this paper we present a non-equilibrium traffic model shown to be devoid of the gas-like behavior that plagues other higher-order models. The system of partial differential equations that describes this model is hyperbolic and has two characteristic fields: one is genuinely nonlinear and the other is linearly degenerate. The first field gives rise to shock and rarefaction waves that are similar to those of the Lighthill–Whitham–Richards (LWR) model, while the second field produces contact discontinuities. All these waves travel no faster than traffic; thus the trajectory of a vehicle cannot be influenced by what happens behind it. The model is also shown to exhibit correct queue-end behavior and is able to explain some of the observed traffic phenomena that challenge old models.