Nous considérons un modèle de trafic autoroutier au second ordre que nous bâtirons à partir de considérations comportementales simples. L'analyse du problème de Riemann afférent sera menée. Dans la seconde partie nous développerons la définition d'une solution obtenue à la limite, issue d'une famille de problèmes perturbés rendant le problème de Riemann toujours solvable. Nous constaterons enfin les conséquences de cette extension en terme de limite de compressibilité et de conservation de quantités comportementales.
In the first part of the Note, we introduce a second order traffic flow model, which we derive from simple physical considerations. We consider the related Riemann problem and solve it in any cases. In the second part, we examine what is required for the construction of proper analytical solutions to be always possible, and what the extended model implies in term of incompressibility, and conservation of physically meaningful quantities.
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@article{CRMATH_2008__346_21-22_1203_0,
author = {Lebacque, Jean Patrick and Louis, Xavier and Mammar, Salim and Schnetzler, Bernard and Haj-Salem, Habib},
title = {Mod\'elisation du trafic autoroutier au second ordre},
journal = {Comptes Rendus. Math\'ematique},
pages = {1203--1206},
publisher = {Elsevier},
volume = {346},
number = {21-22},
year = {2008},
doi = {10.1016/j.crma.2008.09.024},
language = {fr},
url = {http://www.numdam.org/articles/10.1016/j.crma.2008.09.024/}
}
TY - JOUR AU - Lebacque, Jean Patrick AU - Louis, Xavier AU - Mammar, Salim AU - Schnetzler, Bernard AU - Haj-Salem, Habib TI - Modélisation du trafic autoroutier au second ordre JO - Comptes Rendus. Mathématique PY - 2008 SP - 1203 EP - 1206 VL - 346 IS - 21-22 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2008.09.024/ DO - 10.1016/j.crma.2008.09.024 LA - fr ID - CRMATH_2008__346_21-22_1203_0 ER -
%0 Journal Article %A Lebacque, Jean Patrick %A Louis, Xavier %A Mammar, Salim %A Schnetzler, Bernard %A Haj-Salem, Habib %T Modélisation du trafic autoroutier au second ordre %J Comptes Rendus. Mathématique %D 2008 %P 1203-1206 %V 346 %N 21-22 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2008.09.024/ %R 10.1016/j.crma.2008.09.024 %G fr %F CRMATH_2008__346_21-22_1203_0
Lebacque, Jean Patrick; Louis, Xavier; Mammar, Salim; Schnetzler, Bernard; Haj-Salem, Habib. Modélisation du trafic autoroutier au second ordre. Comptes Rendus. Mathématique, Tome 346 (2008) no. 21-22, pp. 1203-1206. doi : 10.1016/j.crma.2008.09.024. http://www.numdam.org/articles/10.1016/j.crma.2008.09.024/
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