On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow

Vincenzo Coscia

doi:10.1016/j.crme.2004.03.016

On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow

Presented by: Évariste Sanchez-Palencia

Vincenzo Coscia ¹

¹ Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy

Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 585-590.

Abstract
Résumé

This Note deals with the development of mathematical methods for the closure of the mass conservation equation for macroscopic hydrodynamical models of traffic flow on roads. The closure is obtained by a phenomenological model, relating the local mean velocity to local density earlier in time. An evolution equation is obtained for the flux and a stability analysis is performed; this qualitatively describes some features of congested flow.

Cette Note est dédiée au dévelopement d'une méthodes mathématiques pour la fermeture des équations macroscopiques de la conservation de la masse, intervenant dans la modélisation du trafic des véhicules. La fermeture est obtenue en utilisant un modèle phénoménologique approprié pour relier la vitesse moyenne locale à la densité locale (avec retard en temp). Une équation pour le flux est derivée et une analyse de stabilité est conduite.

Received: 2004-02-01
Accepted: 2004-03-16
Published online: 2004-06-01

DOI: 10.1016/j.crme.2004.03.016

Keywords: Continuum mechanics, Traffic flow, Continuum models, Nonlinear sciences
Mots-clés : Milieux continus, Flux du traffic, Models continues, Sciences non-linéaires

Author's affiliations:

Vincenzo Coscia ¹

¹ Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy

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Vincenzo Coscia. On a closure of mass conservation equation and stability analysis in the mathematical theory of vehicular traffic flow. Comptes Rendus. Mécanique, Volume 332 (2004) no. 8, pp. 585-590. doi : 10.1016/j.crme.2004.03.016. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2004.03.016/

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