A Multiclass Homogenized Hyperbolic Model of Traffic Flow
A Multiclass Homogenized Hyperbolic Model of Traffic Flow
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DOI：
10.1137/s0036141002411490
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发表时间：
2003
期刊：
影响因子：
--
通讯作者：
P. Bagnerini;M. Rascle
中科院分区：
文献类型：
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作者：
P. Bagnerini;M. Rascle
我们引入了一种新的同质双曲线（多类）交通流模型，它使我们能够考虑不同类型的车辆（汽车、卡车、公共汽车等）和驾驶员的行为。我们用 Godunov 方案离散化下面介绍的起始拉格朗日系统，并且让 (x,t) 中的网格大小 h 趋于 0：（车辆的）典型长度和时间消失。因此，描述交通中不同汽车驾驶员对反应异质性的变量（这里是 (w,a)）在 $h\rightarrow 0$ 时产生较大的振荡。 (w,a) 中的这些（已知）振荡持续存在，我们描述了速度和密度之间的均匀关系。我们证明速度是标量守恒定律的唯一解“la Kruzkov”，具有可变系数，在 x 上不连续。最后，我们证明了相同的宏观均质化模型也是相应的多类Follow-the-Leader模型的流体动力学极限。
We introduce a new homogenized hyperbolic (multiclass) traffic flow model, which allows us to take into account the behaviors of different type of vehicles (cars, trucks, buses, etc.) and drivers. We discretize the starting Lagrangian system introduced below with a Godunov scheme, and we let the mesh size h in (x,t) go to 0: the typical length (of a vehicle) and time vanish. Therefore, the variables---here (w,a)---which describe the heterogeneity of the reactions of the different car-driver pairs in the traffic, develop large oscillations when $h\rightarrow 0$. These (known) oscillations in (w,a) persist in time, and we describe the homogenized relations between velocity and density. We show that the velocity is the unique solution "a la Kruzkov" of a scalar conservation law, with variable coefficients, discontinuous in x. Finally, we prove that the same macroscopic homogenized model is also the hydrodynamic limit of the corresponding multiclass Follow-the-Leader model.