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 = {Jean Patrick Lebacque and Xavier Louis and Salim Mammar and Bernard Schnetzler and Habib Haj-Salem},
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},
}
TY - JOUR AU - Jean Patrick Lebacque AU - Xavier Louis AU - Salim Mammar AU - Bernard Schnetzler AU - Habib Haj-Salem 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 DO - 10.1016/j.crma.2008.09.024 LA - fr ID - CRMATH_2008__346_21-22_1203_0 ER -
%0 Journal Article %A Jean Patrick Lebacque %A Xavier Louis %A Salim Mammar %A Bernard Schnetzler %A Habib Haj-Salem %T Modélisation du trafic autoroutier au second ordre %J Comptes Rendus. Mathématique %D 2008 %P 1203-1206 %V 346 %N 21-22 %I Elsevier %R 10.1016/j.crma.2008.09.024 %G fr %F CRMATH_2008__346_21-22_1203_0
Jean Patrick Lebacque; Xavier Louis; Salim Mammar; Bernard Schnetzler; Habib Haj-Salem. Modélisation du trafic autoroutier au second ordre. Comptes Rendus. Mathématique, Volume 346 (2008) no. 21-22, pp. 1203-1206. doi : 10.1016/j.crma.2008.09.024. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.09.024/
[1] Resurrection of second order models of traffic flows, SIAM J. Math., Volume 60 (2000) no. 3, pp. 916-938
[2] On the role of source terms in continuum traffic flow models, Math. Comp. Modelling, Volume 44 (2006), pp. 917-930
[3] Requiem for second order fluid approximations of traffic flow, Transport. Res. B, Volume 29 (1995), pp. 277-286
[4] A system of non-strictly hyperbolic conservation laws arising in elasticity theory, Arch. Rational Mech. Anal., Volume 72 (1979) no. 3, pp. 219-241
[5] The Aw–Rascle and Zhangh models: Vacuum problems, existence and regularity of the solutions of the Riemann problem, Transport. Res. B, Volume 41 (2007), pp. 710-721
[6] J.P. Lebacque, The Godunov scheme and what it means for first order traffic flows models, in: J.B. Lesort (Ed.), Proceedings of the 13th ISTTT, 1996, pp. 647–678
[7] On kinematic waves II. A theory of traffic flows on long crowed roads, Proc. Roy. Soc. A, Volume 229 (1955), pp. 317-345
[8] S. Mammar, Développement d'un modèle de simulation macro microscopique de simulation du trafic, Thèse de Doctorat, Univ. Evry, 2006
[9] Shock Waves and Reaction–Diffusion Equations, Springer-Verlag, 1983 (pp. 239–336)
[10] An non equilibrium traffic model devoid of gas like behavior, Transport. Res. B, Volume 36 (2002), pp. 275-290
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