The Aw-Rascle vehicular traffic flow model with phase transitions

Mathematical and Computer Modelling

Volumn 44, Issue 3-4, 2006, Pages 287-303

  Goatin, Paola ^a  

^a UNIVERSITÉ DE TOULON   (France)

Author keywords

Continuum traffic models; Hyperbolic conservation laws; Phase transitions; Riemann problem

Indexed keywords

DATA REDUCTION; MATHEMATICAL MODELS; PHASE TRANSITIONS; PROBLEM SOLVING;

CONTINUUM TRAFFIC MODELS; HYPERBOLIC CONSERVATION LAWS; LIGHTHILL-WHITHAM-RICHARDS EQUATION; RIEMANN PROBLEM;

TRAFFIC CONTROL;

EID: 33744910314     PISSN: 08957177     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.mcm.2006.01.016     Document Type: Article

References (28)

1. Helbing D. Traffic and related self-driven many-particle systems. Rev. Modern Phys. 73 (2001) 1067-1141
2. Bellomo N., Coscia V., and Delitala M. On the mathematical theory of vehicular traffic flow I - fluid dynamic and kinetic modelling. Math. Models Methods Appl. Sci. 12 (2002) 1801-1844
3. Klar A., Kũhne R.D., and Wegener R. Mathematical models for vehicular traffic. Surveys Math. Ind. 6 (1996) 215-239
4. Lighthill M.J., and Whitham G.B. On kinematic waves II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. London Ser. A 229 (1955) 317-345
5. Richards P.I. Shock waves on the highway. Oper. Res. 4 (1956) 42-51
6. Kerner B.S. Phase transitions in traffic flow. In: Helbing D., Hermann H., Schreckenberg M., and Wolf D. (Eds). Traffic and Granular Flow '99 (2000), Springer Verlag 253-283
7. Kerner B. The Physics of Traffic (2004), Springer-Verlag
8. Colombo R.M., and Maternini G. A new simulation model for the management of unstable traffic flow. New Technologies and Modeling or Roads Applications to Design and Management vol. SIIV (2004). 888-4532-698
9. Payne H.J. Models of freeway traffic and control. Simulation Council Proc. 28. Math. Models Publ. Sys. (1971) 51-61
10. Whitham G.B. Linear and Nonlinear Waves (1999), John Wiley and Sons, New York
11. Daganzo C.F. Requiem for high-order fluid approximations of traffic flow. Trans. Res. 29B 4 (1995) 277-287
12. Colombo R.M. Hyperbolic phase transitions in traffic flow. SIAM J. Appl. Math. 63 2 (2002) 708-721
13. Aw A., and Rascle M. Resurrection of "second order" models of traffic flow. SIAM J. Appl. Math. 60 (2000) 916-938
14. Aw A., Klar A., Materne T., and Rascle M. Derivation of continuum traffic flow models from microscopic follow-the-leader models. SIAM J. Appl. Math. 63 (2002) 259-278
15. P. Bagnerini, R.M. Colombo, A. Corli, On the role of source terms in continuum traffic flow models, 2004 (preprint)
16. Daganzo C.F., Cassidy M.J., and Bertini R.L. Possible explanations of phase transitions in highway traffic. Trans. Res. A 33 5 (1999) 365-379
17. Temple B. Systems of conservation laws with coinciding shock and rarefaction curves. Contemp. Math. 17 (1983) 143-151
18. R.M. Colombo, P. Goatin, F.S. Priuli, Global well posedness of a traffic flow model with phase transitions, Technical report 05, Laboratoire d'Analyse Nonlinéaire Appliquée et Modélisation, Université du Sud Toulon - Var, 2005
19. Herty M., and Klar A. Simplified dynamics and optimization of large scale traffic networks. Math. Models Methods Appl. Sci. 14 (2004) 579-601
20. J. Goodman, Initial boundary value problems for hyperbolic systems of conservation laws, Ph.D. Thesis, California University, 1982
21. Amadori D., and Colombo R.M. Continuous dependence for 2×2 conservation laws with boundary. J. Differential Equations 138 2 (1997) 229-266
22. F. Berthelin, P. Degond, M. Delitala, M. Rascle, A model for the formation and evolution of traffic jams, Arch. Ration. Mech. Anal. (in press)
23. R.M. Colombo, P. Goatin, Traffic flow models with phase transitions, 2005 (preprint)
24. P. Goatin, Modeling a bottleneck by the Aw-Rascle model with phase transitions, 2005 (preprint)
25. Bressan A. Hyperbolic Systems of Conservation Laws (2000), Oxford University Press
26. Colombo R.M., and Corli A. J. Hyperbolic Differential Equations 1 4 (2004) 725-745
27. Amadori D., and Colombo R.M. Viscosity solutions and standard Riemann semigroup for conservation laws with boundary. Rend. Sem. Mat. Univ. Padova 99 (1998) 219-245
28. Colombo R.M., and Rosini M.D. Well posedness of balance laws with boundary. J. Math. Anal. Appl. 311 2 (2005) 683-702