An n-populations model for traffic flow

European Journal of Applied Mathematics

Volumn 14, Issue 5, 2003, Pages 587-612

  Benzoni Gavage, Sylvie ^a   Colombo, Rinaldo M ^b  

^a UNIVERSITÉ DE LYON   (France)

^b UNIVERSITY OF BRESCIA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0242626883     PISSN: 09567925     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0956792503005266     Document Type: Article

References (32)

1. ANCONA, F. & MARSON, A. (1999) Scalar non-linear conservation laws with integrable boundary data. Nonlinear Anal. 35(6, Ser. A: Theory Methods), 687-710.
2. AW, A. & RASCLE, M. (2000) Resurrection of "second order" models of traffic flow. SIAM J. Appl. Math. 60(3), 916-938.
3. BENZONI-GAVAGE, S. & SERRE, D. (1994) Compacité par compensation pour une classe de systèmes hyperboliques de p ≥ 3 lois de conservation. Rev. Mat. Iberoamericana, 10(3), 557-579.
4. BRESSAN, A. (2000) Hyperbolic Systems of Conservation Laws. Oxford University Press.
5. CHANUT, S. (2003) Vers une modélisation macroscopique d'un écoulement bi-fluide poids lourds et véhicules légers. PhD thesis, ENTPE, Vaulx en Velin, France (in preparation).
6. COLOMBO, R. M. (2002) On a 2 × 2 hyperbolic traffic flow model. Mathematical and Computer Modelling, 35, 683-688.
7. COLOMBO, R. M. & CORLI, A. (2002) Sonic hyperbolic phase transitions and Chapman-Jouguet detonations. J. Diff. Eq. 184(2), 321-347.
8. DAFERMOS, C. M. (2000) Hyperbolic Conservation Laws in Continuum Physics. Springer-Verlag.
9. DAGANZO, C. F. (1995) Requiem for high-order fluid approximations of traffic flow. Trans. Res.
10. DAGANZO, C. F. (2002) A behavioral theory of multi-lane traffic flow. Part I: Long homogeneous freeway sections. Trans. Res.
11. DELLAR, J. (2003) Compound waves in a thermodynamic lattice BGK scheme using non-perturbative equilibria. Europhys. Lett. (to appear).
12. HEIDEMANN, D. (1999) Some critical remarks on a class of traffic flow models. Trans. Res. B, 33, 153-155.
13. HOFF, D. (1985) Invariant regions for systems of conservation laws. Trans. Am. Math. Soc., 289(2), 591-610.
14. HOLLAND, E. N. & WOODS, A. W. (1997) A continuum model for the dispersion of traffic on two-lane roads. Transportation Res. B, 31, 473-485.
15. HOOGENDOORN, S. (1999) Multiclass continuum modelling of multilane traffic flow. PhD thesis, Delft University of Technology.
16. KERNER, B. S. & KONHÄUSER, P. (1993) Cluster effect in initially homogeneous traffic flow. Phys. Rev. E, 48(4), 2335-2338.
17. KEYFITZ, B. L. & KRANZER, H. C. (1979-1980) A system of nonstrictly hyperbolic conservation laws arising in elasticity theory. Arch. Rational Mech. Anal. 72(3), 219-241.
18. KLAR, A. & WEGENER, R. (1999) A hierarchy of models for multilane vehicular traffic. I. Modeling. SIAM J. Appl. Math. 59(3), 983-1001 (electronic).
19. KLAR, A. & WEGENER, R. (1999) A hierarchy of models for multilane vehicular traffic. II. Numerical investigations. SIAM J. Appl. Math. 59(3), 1002-1011 (electronic).
20. KLAR, A. & WEGENER, R. (2000) Kinetic traffic flow models. Modeling in Applied Sciences, pp. 263-316. Birkhäuser Boston.
21. LEVEQUE, R. J. (2002) Finite Volume Methods for Hyperbolic Problems. Cambridge Texts in Applied Mathematics. Cambridge University Press.
22. LIGHTHILL, M. J. & WHITHAM, G. B. (1955) On kinematic waves. II. A theory of traffic flow on long crowded roads. Proc. Roy. Soc. Land A. 229, 317-345.
23. Liu, T. P. (1974) The Riemann problem for general 2 × 2 conservation laws. Trans. Am. Math. Soc. 199, 89-112.
24. MICHALOPOULOS, P. G., BESKOS, D. E. & YAMAUCHI, Y. (1984) Multilane traffic flow dynamics: some macroscopic considerations. Transportation Res. B, 18(4-5), 377-395.
25. RICHARDS, P. I. (1956) Shock waves on the highway. Operations Res. 4, 42-51.
26. SERRE, D. (1999-2000) Systems of Conservation Laws. 1-2. (Translated from the 1996 French original by I. N. Sneddon.) Cambridge University Press.
27. SERRE, D. (2002) Matrices. Theory and Applications. Springer.
28. SHEARER, M., SCHAEFFER, D. G., MARCHESIN, D. & PAES-LEME, P. L. (1987) Solution of the Riemann problem for a prototype 2 × 2 system of nonstrictly hyperbolic conservation laws. Arch. Rat. Mech. Anal. 97(4), 299-320.
29. SMOLLER, J. (1994) Shock Waves and Reaction-diffusion Equations, 2nd ed. Springer-Verlag.
30. WONG, G. C. K. & WONG, S. C. (2002) A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers. Transportation Res. A, 36, 827-841.
31. ZHANG, H. M. (2002) A theory of nonequilibrium traffic flow. Transportation Res. B, 32(7), 485-498.
32. ZHANG, H. M. & JIN, W. L. (2002) A kinematic wave traffic flow model for mixed traffic. Transportation Research Board, 81st Annual Meeting, Washington, DC.