Free-congested and micro-macro descriptions of traffic flow

Francesca Marcellini

doi:10.3934/dcdss.2014.7.543

Article Contents

2014, Volume 7, Issue 3: 543-556. Doi: 10.3934/dcdss.2014.7.543

This issue Previous Article Efficient robust control of first order scalar conservation laws using semi-analytical solutions Next Article Computing travel times from filtered traffic states

Free-congested and micro-macro descriptions of traffic flow

Francesca Marcellini^1,

1.
Università di Milano-Bicocca, Dipartimento di Matematica e Applicazioni, Via Cozzi 53, 20125 Milano

Received: April 30, 2013

Revised: June 30, 2013

Published: May 2014

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Abstract

We present two frameworks for the description of traffic, both consisting in the coupling of systems of different types. First, we consider the Free--Congested model [7,11], where a scalar conservation law is coupled with a $2\times2$ system. Then, we present the coupling of a micro- and a macroscopic models, the former consisting in a system of ordinary differential equations and the latter in the usual LWR conservation law, see [10]. A comparison between the two different frameworks is also provided.

Keywords:

Traffic models,
hyperbolic systems of conservation laws,
macroscopic traffic models,
ordinary differential equations,
microscopic traffic models.

Mathematics Subject Classification: 35L65, 90B20.

Citation:

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