A new second-order traffic model is derived from a nonlinear Vlasov type equation with a source term. The homogeneous part of the system is proven to be hyperbolic. Using a vehicle speed relaxation source term the full system appears to be conditionally linearly stable with instabilities in the dense traffic region. The stability condition depends on the choice of the source term and the model parameters. Numerical experiments confirm the analysis. For a class of source terms, the system is unconditionally linearly stable but numerical experiments show the appearance of nonlinear instabilities that evolve into stop-and-go waves in the dense region.
Dans cette Note, un modèle de trafic du second ordre est construit à partir d'une description cinétique de type Vlasov. La partie homogène de ce système est hyperbolique. Néanmoins, en utilisant un terme source de relaxation de vitesse, le système complet non homogène s'avère être conditionnellement linéairement stable avec une région d'instabilité localisée dans le régime dense. La condition de stabilité linéaire dépend du choix du terme source et des paramètres ouverts du modèle. Les expériences numériques confirment l'analyse théorique. Pour une certaine classe de termes de source, le système est inconditionnellement linéairement stable ; les expérimentations numériques montrent l'apparition d'instabilités non linéaires qui évoluent en ondes « stop-and-go » dans la région de trafic dense.
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Mots-clés : Systèmes dynamiques, Modèle de trafic, Équation cinétique, Équation hyperbolique, Stabilité linéaire, Stop-and-go, Schéma numérique
Romain Billot 1, 2; Christophe Chalons 2; Florian De Vuyst 2, 3, 4; Nour-Eddin El Faouzi 1; Jacques Sau 5
@article{CRMECA_2010__338_9_529_0,
author = {Romain Billot and Christophe Chalons and Florian De Vuyst and Nour-Eddin El Faouzi and Jacques Sau},
title = {A conditionally linearly stable second-order traffic model derived from a {Vlasov} kinetic description},
journal = {Comptes Rendus. M\'ecanique},
pages = {529--537},
publisher = {Elsevier},
volume = {338},
number = {9},
year = {2010},
doi = {10.1016/j.crme.2010.07.018},
language = {en},
}
TY - JOUR AU - Romain Billot AU - Christophe Chalons AU - Florian De Vuyst AU - Nour-Eddin El Faouzi AU - Jacques Sau TI - A conditionally linearly stable second-order traffic model derived from a Vlasov kinetic description JO - Comptes Rendus. Mécanique PY - 2010 SP - 529 EP - 537 VL - 338 IS - 9 PB - Elsevier DO - 10.1016/j.crme.2010.07.018 LA - en ID - CRMECA_2010__338_9_529_0 ER -
%0 Journal Article %A Romain Billot %A Christophe Chalons %A Florian De Vuyst %A Nour-Eddin El Faouzi %A Jacques Sau %T A conditionally linearly stable second-order traffic model derived from a Vlasov kinetic description %J Comptes Rendus. Mécanique %D 2010 %P 529-537 %V 338 %N 9 %I Elsevier %R 10.1016/j.crme.2010.07.018 %G en %F CRMECA_2010__338_9_529_0
Romain Billot; Christophe Chalons; Florian De Vuyst; Nour-Eddin El Faouzi; Jacques Sau. A conditionally linearly stable second-order traffic model derived from a Vlasov kinetic description. Comptes Rendus. Mécanique, Volume 338 (2010) no. 9, pp. 529-537. doi : 10.1016/j.crme.2010.07.018. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.018/
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