Analytic approach to the critical density in cellular automata for traffic flow

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 60, Issue 1, 1999, Pages 188-196

  Gerwinski, M ^a   Krug, J ^a  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

APPROXIMATION THEORY; BOUNDARY CONDITIONS; CELLULAR RADIO SYSTEMS; COMPUTER SIMULATION; FINITE AUTOMATA; PIECEWISE LINEAR TECHNIQUES; RANDOM PROCESSES;

JAM DISSOLUTION; STOCHASTIC TRAFFIC CELLULAR AUTOMATON (STCA);

HIGHWAY TRAFFIC CONTROL;

EID: 0032620970     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.60.188     Document Type: Article

References (38)

1. Traffic and Granular Flow, edited by D.E. Wolf, M. Schreckenberg, and A. Bachem (World Scientific, Singapore, 1996).
2. Traffic and Granular Flow ‘97, edited by M. Schreckenberg and D.E. Wolf (Springer, Singapore, 1998).
3. D. Helbing, Verkehrsdynamik: Neue physikalische Modellierungskonzepte (Springer, Berlin, 1997).
4. J. Krug, Phys. Rev. Lett. 67, 1882 (1991)
5. Phys. Rev. Lett.M.R. Evans, D.P. Foster, C. Godréche, and D. Mukamel, 74, 208 (1995)
6. Phys. Rev. Lett.M.R. Evans, Y. Kafri, H.M. Koduvely, and D. Mukamel, 80, 425 (1998).
7. K. Nagel and M. Schreckenberg, J. Phys. I 2, 2221 (1992).
8. K. Nagel, Phys. Rev. E 53, 4655 (1996).
9. K. Nagel and H.J. Herrmann, Physica A 199, 254 (1993).
10. K. Nagel, Int. J. Mod. Phys. C 5, 567 (1994).
11. S. Wolfram, Rev. Mod. Phys. 55, 601 (1983).
12. J. Krug and H. Spohn, Phys. Rev. A 38, 4271 (1988).
13. O. Biham, A.A. Middleton, and D. Levine, Phys. Rev. A 46, R6124 (1992).
14. V. Belitsky and P.A. Ferrari, J. Stat. Phys. 80, 517 (1995).
15. Y. Elskens and H.L. Frisch, Phys. Rev. A 31, 3812 (1985).
16. Already the presence of three velocities leads to completely different behavior, see P. Krapivsky, S. Redner, and F. Leyvraz, Phys. Rev. E 51, 3977 (1995).
17. L.C.Q. Vilar and A.M.C. de Souza, Physica A 211, 84 (1994).
18. B. Eisenblätter, L. Santen, A. Schadschneider, and M. Schreckenberg, Phys. Rev. E 57, 1309 (1998).
19. G. Csányi and J. Kertész, J. Phys. A 28, L427 (1995)
20. J. Phys. AG. CsányiJ. Kertész29, 471(E) (1996).
21. M. Sasvári and J. Kertész, Phys. Rev. E 56, 4104 (1997).
22. D. Chowdhury, K. Ghosh, A. Majumdar, S. Sinha, and R.B. Stinchcombe, Physica A 246, 471 (1997).
23. S. Lübeck, M. Schreckenberg, and K.D. Usadel, Phys. Rev. E 57, 1171 (1998);and in 2, p. 361.
24. L. Roters, Diploma thesis, University of Duisburg, 1998 (unpublished).
25. S. Lübeck, L. Roters, and K.D. Usadel, in 2, p. 355.
26. H. Yaguchi, Hiroshima Math. J. 16, 449 (1986).
27. A. Schadschneider and M. Schreckenberg, J. Phys. A 26, L679 (1993).
28. M. Schreckenberg, A. Schadschneider, K. Nagel, and N. Ito, Phys. Rev. E 51, 2939 (1995).
29. J. Krug and P.A. Ferrari, J. Phys. A 29, L465 (1996).
30. M.J. Lighthill and G.B. Whitham, Proc. R. Soc. London, Ser. A 229, 317 (1955).
31. H. van Beijeren, R. Kutner, and H. Spohn, Phys. Rev. Lett. 54, 2026 (1985).
32. D. Forster, D.R. Nelson, and M.J. Stephen, Phys. Rev. A 16, 732 (1977).
33. M. Kardar, G. Parisi, and Y.C. Zhang, Phys. Rev. Lett. 56, 889 (1986).
34. T. Nagatani, J. Phys. A 28, 7079 (1995).
35. J. Krug and H. Spohn, Europhys. Lett. 8, 219 (1989).
36. K. Nagel and M. Paczuski, Phys. Rev. E 51, 2909 (1995).
37. B. Eisenblätter, Diploma thesis, University of Duisburg, 1996 (unpublished).
38. In many cases (Formula presented) was observed to be close to the critical density (Formula presented) of the deterministic model.