Macroscopic Modeling of Multilane Motorways Using a Two-Dimensional Second-Order Model of Traffic Flow
Macroscopic Modeling of Multilane Motorways Using a Two-Dimensional Second-Order Model of Traffic Flow
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DOI：
10.1137/17m1151821
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发表时间：
2017-10
期刊：
影响因子：
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通讯作者：
M. Herty;S. Moutari;G. Visconti
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文献类型：
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作者：
M. Herty;S. Moutari;G. Visconti
变道是高速公路上最常见的操作之一。虽然宏观交通模型适合描述快速移动的拥挤交通，但这些模型大多是在一维框架内发展起来的，因此在某种程度上忽略了换道行为。本文在Aw and Rascle[Aw and Rascle，SIAM J.Appl.Math，2000]和Zhang[Zhang，Transport.Res.B-Meth，2002]宏观交通流模型的基础上，提出了一种考虑高速公路换道行为的宏观模型。在条件下，当变道机动不再可能时，该模型就“松弛”到一维Aw-Rascle-Zhang模型。遵循与[Aw，Klar，Matne和Rascle，SIAM J.Appl.Math，2002]相同的方法，我们通过对具有驱动方向的微观跟随-领先者模型的时间离散化的尺度来推导出二维宏观模型。我们对所提出的宏观问题的时空离散化进行了详细的分析，并给出了相关黎曼问题解的近似解。此外，我们还通过一些数值实验说明了该模型的一些特点。
Lane changing is one of the most common maneuvers on motorways. Although, macroscopic traffic models are well known for their suitability to describe fast moving crowded traffic, most of these models are generally developed in one dimensional framework, henceforth lane changing behavior is somehow neglected. In this paper, we propose a macroscopic model, which accounts for lane-changing behavior on motorway, based on a two-dimensional extension of the Aw and Rascle [Aw and Rascle, SIAM J.Appl.Math., 2000] and Zhang [Zhang, Transport.Res.B-Meth., 2002] macroscopic model for traffic flow. Under conditions, when lane changing maneuvers are no longer possible, the model "relaxes" to the one-dimensional Aw-Rascle-Zhang model. Following the same approach as in [Aw, Klar, Materne and Rascle, SIAM J.Appl.Math., 2002], we derive the two-dimensional macroscopic model through scaling of time discretization of a microscopic follow-the-leader model with driving direction. We provide a detailed analysis of the space-time discretization of the proposed macroscopic as well as an approximation of the solution to the associated Riemann problem. Furthermore, we illustrate some features of the proposed model through some numerical experiments.