SIAM Journal on Mathematical Analysis, Volume 53, Issue 1, Page 309-322, January 2021.
The goal of this paper is to derive rigorously macroscopic traffic flow models from microscopic models. More precisely, for the microscopic models, we consider follow-the-leader type models with different types of drivers and vehicles which are distributed randomly on the road. After a rescaling, we show that the cumulative distribution function converges to the solution of a macroscopic model. We also establish a connection between this macroscopic model and the so-called Lighthill--Whitham--Richards model.

中文翻译：

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从异构微观交通流模型到宏观模型

SIAM数学分析杂志，第53卷，第1期，第309-322页，2021
年1月。本文的目的是从微观模型中严格得出宏观交通流量模型。更准确地说，对于微观模型，我们考虑跟随者类型的模型，其中驾驶员和车辆的类型不同，它们随机分布在道路上。重新缩放后，我们表明累积分布函数收敛到宏观模型的解。我们还在此宏观模型与所谓的Lighthill-Whitham-Richards模型之间建立了联系。