A new multi-class continuum model for traffic flow

Transportmetrica

Volumn 3, Issue 1, 2007, Pages 73-85

  Gupta, A K ^a   Katiyar, V K ^a  

^a INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

Author keywords

Continuum model; Heterogeneous drivers; Platoon dispersion; Traffic flow

Indexed keywords

EID: 42549107198     PISSN: 18128602     EISSN: None     Source Type: Journal    
DOI: 10.1080/18128600708685665     Document Type: Article

References (33)

1. Aw, A. and Rascle, M. (2000) Resurrection of second order models of traffic flow. SIAM Journal of Applied Mathematics, 60, 916-938.
2. Bellomo, N., Delitala M. and Coscia V. (2002) On the mathematical theory of vehicular traffic flow I: fluid dynamic and kinetic modeling. Mathematical Models and Methods in Applied Sciences, 12, 1801-1843.
3. Berg, P., Mason, A. and Woods A. (2000) Continuum approach to car-following models. Physical Review E, 61, 1056-1066.
4. Cho, H.J. and Lo, S.C. (2002) Modeling self-consistent multi-class dynamic traffic flow. Physica A, 312, 342-362.
5. Daganzo, C.F. (1995) The cell-transmission model, Part II: network traffic. Transportation Research Part B, 29, 79-94.
6. Daganzo, C.F. (1997) A continuum theory of traffic dynamics for freeways with special lanes. Transportation Research Part B, 31, 83-102.
7. Daganzo, C.F. (2002) A behavioral theory of multi-lane traffic flow, Part I: long homogeneous freeway sections. Transportation Research Part B, 36, 131-158.
8. Drake, J.S., Schofer, J.L. and May, A.D. (1967) A statistical analysis of speed density hypothesis. Highway Research Record, 154, 53-87.
9. Fukui, M., Sugiyama, Y., Schreckenberg, M. and Wolf, D.E. (2003) Traffic and Granular Flow’01. Springer-Verlag, Berlin Heidelberg.
10. Gerlough, D.L. and Huber, M.J. (1975) Special Report No. 165. Transportation Research Board, National Research Council, Washington, D.C.
11. Gupta, A.K. and Katiyar, V.K. (2005) Analyses of shock wave and jams in traffic flow. Journal of Physics A, 38, 4069-4083.
12. Gupta, A.K. and Katiyar, V.K. (2006) A new anisotropic continuum model for traffic flow. Physica A, 368, 551-559.
13. Helbing, D. (1997) Verkehrsdynamik. Springer, Berlin.
14. Helbing, D. (2001) Traffic and related self-driven many-particle systems. Reviews of Modern Physics, 73, 1067-1141.
15. Herrmann, M., Kerner, B.S. (1998) Local cluster effect in different traffic flow models. Physica A, 255, 163-188.
16. Hoogendoorn, S.P. and Bovy, P.H.L. (1996) Proceedings of the Second TRAIL Annual Congress.
17. Hoogendoorn, S.P. and Bovy, P.H.L. (2000) Continuum modeling of multiclass traffic flow. Transportation Research Part B, 34, 123-146.
18. Jiang, R., Wu, Q. and Zhu, Z. (2002) A new continuum model for traffic flow and numerical tests. Transportation Research Part B, 36, 405-419.
19. Kerner, B.S. and Konhauser, P. (1993) Cluster effect in initially homogeneous traffic flow. Physical Review E, 48, 2335-2338.
20. Lee, H.K., Lee, H.W. and Kim, D. (2001) Macroscopic traffic models from microscopic car-following models. Physical Review E, 64, 056-126.
21. Lighthill, M.J. and Whitham, G.B. (1955) On kinetic waves, II: a theory of traffic flow on long crowed roads. Proceedings of the Royal Society of London, Series A, 229, 317-345.
22. Mason A.D. and Woods A.W. (1997) Car-following model of multispecies systems of road traffic. Physical Review E, 55, 2203-2214.
23. Munjal, P.K. and Pipes, L.A. (1971) Propagation of onramp density perturbations on unidirectional two- and three-lane freeways. Transportation Research, 5, 241-255.
24. Payne, H.J. (1971) Models of freeway traffic and control. In G.A. Bekey (ed.), Mathematical Models of Public Systems, Simulation Councils Proc. Ser., Vol. 1, pp. 51-60.
25. Phillips, W.F. (1979) A kinetic model for traffic flow with continuum implications. Transportation Planning and Technology, 5, 131-138.
26. Richards, P.I. (1956) Shock waves on the highway. Operations Research, 4, 42-51.
27. Shu, C.W. (1997) Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws. ICASE Report No. 97-65.
28. Wong, G.C.K. and Wong, S.C. (2002) A multi-class traffic flow model - an extension of LWR model with heterogeneous drivers. Transportation Research Part A, 36, 827-841.
29. Zhang, H.M. (1998) A theory of nonequilibrium traffic flow. Transportation Research Part B, 32, 485-498.
30. Zhang, H.M. (2002) A non-equilibrium traffic flow model devoid of gas-like behavior. Transportation Research Part B, 36, 275-290.
31. Zhang, H.M. (2003) Driver memory, traffic viscosity and a viscous vehicular traffic model. Transportation Research Part B, 37, 27-41.
32. Zhang, M.P., Wong, S.C. and Shu, C.W. (2006) A weighted essentially non-oscillatory numerical scheme for a multi-class traffic flow model on an inhomogeneous highway. Journal of Computational Physics, 212, 739-756.
33. Zhou, X., Liu, Z. and Luo, J. (2002) The density wave in a car-following model. Journal of Physics A, 35, 4495-4500.