The Aw-Rascle and Zhang's model: Vacuum problems, existence and regularity of the solutions of the Riemann problem

Transportation Research Part B: Methodological

Volumn 41, Issue 7, 2007, Pages 710-721

  Lebacque, Jean Patrick ^a   Mammar, Salim ^a   Haj Salem, Habib ^a  

^a French National Institute for Transport and Safety Research   (France)

Author keywords

Analytical solutions; Contact discontinuities; Fundamental diagram; Rarefaction waves; Riemann problem; Shock waves; Vacuum problems

Indexed keywords

MATHEMATICAL MODELS; OPTIMAL CONTROL SYSTEMS; SHOCK WAVES; VACUUM TECHNOLOGY;

CONTACT DISCONTINUITIES; FUNDAMENTAL DIAGRAM; RAREFACTION WAVES; RIEMANN PROBLEM;

GAS DYNAMICS;

FLOW MODELING; NUMERICAL METHOD; TRANSPORTATION;

EID: 34247377825     PISSN: 01912615     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.trb.2006.11.005     Document Type: Article

References (10)

1. Aw A., and Rascle M. Resurrection of second order models of traffic flow. SIAM Journal of Applied Mathematics 60 3 (2000) 916-938
2. Daganzo C.F. Requiem for second-order fluid approximations of traffic flow. Transportation Research Part B 29 (1995) 277-286
3. Del Castillo J.-M., Pintado P., and Benitz F.G. A formulation of reaction time of traffic flow models. In: Daganzo C.F. (Ed). Proceeding of the 12th International Symposium on Transportation and Traffic Flow Theory (1993), Pergamon, Berkeley, Amsterdam 387-405
4. Kröner D. Numerical Schemes for Conservation Laws (1997), Wiley Teubner
5. Lebacque, J.P., Mammar, S., Haj-Salem, H., 2005. Second order traffic flow modeling: supply-demand analysis of the inhomogeneous Riemann problem and of boundary conditions. In: Proceedings of the Euro Working Group on Transportation, Poznan.
6. Mammar, S., Lebacque, J.P., Haj-Salem, H., 2005. Second order traffic flow modelling: the Riemann problem resolution in the homogeneous case without relaxation term. In: Proceedings of the Euro Working Group on Transportation, Poznan.
7. Payne H.J. Models of freeway traffic and control. Mathematical Models of Public Systems. Simulation Council Proceedings Series 28 1 (1971) 51-61
8. Ross P. Traffic dynamics. Transportation Research Part B 22 6 (1988) 421-435
9. Zhang H.M. A theory of nonequilibrium traffic flow. Transportation Research Part B 32 (1998) 485-498
10. Zhang H.M. A non-equilibrium traffic model devoid of gas-like behavior. Transportation Research Part B 36 (2002) 275-290