First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow

Nicola Bellomo; Vincenzo Coscia

doi:10.1016/j.crme.2005.09.004

First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow
[Modèles du premier ordre et fermeture de l'équation de conservation de masse dans la théorie mathématique du trafic routier]

Nicola Bellomo ¹ ; Vincenzo Coscia ²

¹ Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
² Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy

Comptes Rendus. Mécanique, Volume 333 (2005) no. 11, pp. 843-851.

Résumé
Abstract

Ce article propose une revue et une analyse critique des modèles hydrodynamiques du trafic routier obtenus par fermeture de l'équation de conservation de la masse. La fermeture est obtenue à partir de modèles phénoménologiques reliant les profils des densités locales à la vitesse moyenne locale. Différents modèles sont décrits et discutés aussi bien dans le cas déterministe que stochastique. L'analyse est développée en vue d'applications aux simulations des modèles de trafic pour les réseaux routiers. Des perspectives de recherche, basées sur notre analyse, sont proposées dans la dernière partie de ce travail.

This article deals with a review and critical analysis of first order hydrodynamic models of vehicular traffic flow obtained by the closure of the mass conservation equation. The closure is obtained by phenomenological models suitable to relate the local mean velocity to local density profiles. Various models are described and critically analyzed in the deterministic and stochastic case. The analysis is developed in view of applications of the models to traffic flow simulations for networks of roads. Some research perspectives are derived from the above analysis and proposed in the last part of the paper.

Publié le : 2005-10-14

DOI : 10.1016/j.crme.2005.09.004

Keywords: Continuum mechanics, Traffic flow models, Mass conservation, Continuum models, Nonlinear sciences
Mots-clés : Milieux continus, Modèles de trafic routier, Équation de conservation de la masse, Modèles continus, Nonlinéarité

Affiliations des auteurs :

Nicola Bellomo ¹ ; Vincenzo Coscia ²

¹ Dipartimento di Matematica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
² Dipartimento di Matematica, Università di Ferrara, Via Machiavelli 35, 44100 Ferrara, Italy

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     title = {First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow},
     journal = {Comptes Rendus. M\'ecanique},
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     year = {2005},
     doi = {10.1016/j.crme.2005.09.004},
     language = {en},
}

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Nicola Bellomo; Vincenzo Coscia. First order models and closure of the mass conservation equation in the mathematical theory of vehicular traffic flow. Comptes Rendus. Mécanique, Volume 333 (2005) no. 11, pp. 843-851. doi : 10.1016/j.crme.2005.09.004. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2005.09.004/

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