Macroscopic limits of non-local kinetic descriptions of vehicular traffic

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2022-06-02 DOI:10.3934/krm.2022038

F. A. Chiarello, A. Tosin

引用次数: 6

Abstract

We study the derivation of macroscopic traffic models out of optimal speed and follow-the-leader particle dynamics as hydrodynamic limits of non-local Povzner-type kinetic equations. As a first step, we show that optimal speed vehicle dynamics produce a first order macroscopic model with non-local flux. Next, we show that non-local follow-the-leader vehicle dynamics have a universal macroscopic counterpart in the second order Aw-Rascle-Zhang traffic model, at least when the non-locality of the interactions is sufficiently small. Finally, we show that the same qualitative result holds also for a general class of follow-the-leader dynamics based on the headway of the vehicles rather than on their speed. We also investigate the correspondence between the solutions to particle models and their macroscopic limits by means of numerical simulations.

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车辆交通非局部动力学描述的宏观极限

本文研究了以最优速度和随先粒子动力学作为非局部波兹纳型动力学方程水动力极限的宏观交通模型的推导。作为第一步，我们证明了最优速度车辆动力学产生具有非局部通量的一阶宏观模型。其次，我们证明了在二阶aw - rasle - zhang交通模型中，非局域跟随车辆动力学具有普遍的宏观对应物，至少当相互作用的非局域性足够小时是如此。最后，我们证明了同样的定性结果也适用于基于车辆车头时距而不是速度的一般类型的跟随者动力学。我们还用数值模拟的方法研究了粒子模型解与其宏观极限之间的对应关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.