Lane changing is one of the most common maneuvers on motorways. Although,macroscopic traffic models are well known for their suitability to describefast moving crowded traffic, most of these models are generally developed inone dimensional framework, henceforth lane changing behavior is somehowneglected. In this paper, we propose a macroscopic model, which accounts forlane-changing behavior on motorway, based on a two-dimensional extension of theAw and Rascle [Aw and Rascle, SIAM J.Appl.Math., 2000] and Zhang [Zhang,Transport.Res.B-Meth., 2002] macroscopic model for traffic flow. Underconditions, when lane changing maneuvers are no longer possible, the model"relaxes" to the one-dimensional Aw-Rascle-Zhang model. Following the sameapproach as in [Aw, Klar, Materne and Rascle, SIAM J.Appl.Math., 2002], wederive the two-dimensional macroscopic model through scaling of timediscretization of a microscopic follow-the-leader model with driving direction.We provide a detailed analysis of the space-time discretization of the proposedmacroscopic as well as an approximation of the solution to the associatedRiemann problem. Furthermore, we illustrate some features of the proposed modelthrough some numerical experiments.
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机译：换车道是高速公路上最常见的操作之一。尽管宏观交通模型因其适合描述快速移动的拥挤交通而广为人知，但这些模型中的大多数通常是在一个维度的框架中开发的，因此在某种程度上可以忽略车道变化行为。在本文中，我们基于aw和Rascle [Aw and Rascle，SIAM J.Appl.Math。，2000]和Zhang [Zhang，2000]的二维扩展，提出了一个宏观模型，该模型解释了高速公路上车道的变化行为。 Transport.Res.B-Meth。，2002年）。在条件下，当不再可能进行变道操作时，模型将“放松”到一维Aw-Rascle-Zhang模型。遵循与[Aw，Klar，Materne and Rascle，SIAM J.Appl.Math。，2002]中相同的方法，通过按驱动方向对微观跟随者领导模型的时间离散化进行比例缩放，得出二维宏观模型。提供了对所建议的宏观镜的时空离散化的详细分析，以及对相关黎曼问题的近似解。此外，我们通过一些数值实验说明了所提出模型的一些特征。
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