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Theoretical vs. empirical classification and prediction of congested traffic states

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Abstract

Starting from the instability diagram of a traffic flow model, we derive conditions for the occurrence of congested traffic states, their appearance, their spreading in space and time, and the related increase in travel times. We discuss the terminology of traffic phases and give empirical evidence for the existence of a phase diagram of traffic states. In contrast to previously presented phase diagrams, it is shown that “widening synchronized patterns” are possible, if the maximum flow is located inside of a metastable density regime. Moreover, for various kinds of traffic models with different instability diagrams it is discussed, how the related phase diagrams are expected to approximately look like. Apart from this, it is pointed out that combinations of on- and off-ramps create different patterns than a single, isolated on-ramp.

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References

  1. J. Treiterer, J. Myers, in Proc. 6th Int. Symp. on Transportation and Traffic Theory, edited by D. Buckley (Elsevier, New York, 1974), p. 13

  2. Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki, S. Yukawa, New J. Phys. 10, 033001 (2008)

  3. B. Kerner, H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)

  4. D. Helbing, A. Hennecke, M. Treiber, Phys. Rev. Lett. 82, 4360 (1999)

  5. A. Kesting, M. Treiber, M. Schönhof, D. Helbing, Transportation Research Part C: Emerging Technologies 16, 668 (2008)

  6. A. Kesting, M. Treiber, D. Helbing, Transportation Research Record 1999, 86 (2007)

  7. M. Schönhof, D. Helbing, Transportation Science 41, 1 (2007)

  8. D. Helbing, B. Tilch, Eur. Phys. J. B (2009), DOI: 10.1140/epjb/e2009-00092-8

  9. M. Treiber, D. Helbing, Cooperative Transportation Dynamics 1, 3.1 (2002), (Internet Journal, www.TrafficForum.org/journal)

  10. M. Treiber, A. Hennecke, D. Helbing, Phys. Rev. E 62, 1805 (2000)

  11. H.Y. Lee, H.W. Lee, D. Kim, Phys. Rev. E 59, 5101 (1999)

  12. H. Lee, H. Lee, D. Kim, Phys. Rev. E 62, 4737 (2000)

  13. R. Barlovic, T. Huisinga, A. Schadschneider, M. Schreckenberg, Phys. Rev. E 66, 046113 (2002)

  14. R. Jiang, Q. Wu, B. Wang, Phys. Rev. E 66, 36104 (2002)

  15. B.S. Kerner, The Physics of Traffic (Springer, Heidelberg, 2004)

  16. B. Kerner, S. Klenov, J. Phys. A: Mathematical and General 35, L31 (2002)

  17. P.F. Arndt, Phys. Rev. Lett. 84, 814 (2000)

  18. R. Kubo, Reports of Progress in Physics 29, 255 (1966)

  19. M. Treiber, D. Helbing, Eur. Phys. J. B (2009), DOI: 10.1140/epjb/e2009-00121-8

  20. M. Evans, Y. Kafri, H. Koduvely, D. Mukamel, Phys. Rev. Lett. 80, 425 (1998)

  21. S. Lübeck, M. Schreckenberg, K.D. Usadel, Phys. Rev. E 57, 1171 (1998)

  22. J. Krug, Phys. Rev. Lett. 67, 1882 (1991)

  23. G. Schütz, E. Domany, J. Stat. Phys. 72, 277 (1993)

  24. V. Popkov, L. Santen, A. Schadschneider, G.M. Schütz, J. Phys. A: Mathematical General 34, L45 (2001)

  25. M. Treiber, A. Kesting, D. Helbing, Physica A 360, 71 (2006)

  26. M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, Phys. Rev. E 58, 5429 (1998)

  27. M. Treiber, A. Hennecke, D. Helbing, Phys. Rev. E 59, 239 (1999)

  28. B. Kerner, P. Konhäuser, Phys. Rev. E 48, 2335 (1993)

  29. H. Lee, H. Lee, D. Kim, Phys. Rev. Lett. 81, 1130 (1998)

  30. D. Helbing, Rev. Mod. Phys. 73, 1067 (2001)

  31. D. Helbing, A. Hennecke, V. Shvetsov, M. Treiber, Mathematical and Computer Modelling 35, 517 (2002)

  32. B. Kerner, S. Klenov, J. Phys. A 35, L31 (2002)

  33. B. Kerner, H. Rehborn, Phys. Rev. E 53, R1297 (1996)

  34. D. Helbing, M. Moussaid, Eur. Phys. J. B (2009), DOI: 10.1140/epjb/e2009-00042-6

  35. M. Treiber, A. Kesting, D. Helbing, Transportation Research Part B: Methodology, submitted (2008)

  36. G.B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, New York, 1974), ISBN: 0471940909

  37. M. Lighthill, G. Whitham, Proc. Roy. Soc. London A 229, 317 (1955)

  38. D. Helbing, J. Phys. A 36, L593 (2003)

  39. B. Kerner, Phys. Rev. Lett. 81, 3797 (1998)

  40. B. Kerner, H. Rehborn, Phys. Rev. E 53, R4275 (1996)

  41. D. Helbing, B. Tilch, Phys. Rev. E 58, 133 (1998)

  42. E. Brockfeld, R.D. Kühne, A. Skabardonis, P. Wagner, Transportation Research Record 1852, 124 (2003)

  43. E. Brockfeld, R.D. Kühne, P. Wagner, Transportation Research Record 1876, 62 (2004)

  44. S. Ossen, S.P. Hoogendoorn, Transportation Research Record 1934, 13 (2005)

  45. S. Ossen, S.P. Hoogendoorn, B.G. Gorte, Transportation Research Record 1965, 121 (2007)

  46. A. Kesting, M. Treiber, Transportation Research Record 2088, 148 (2008)

  47. F. Siebel, W. Mauser, Phys. Rev. E 73, 66108 (2006)

  48. B. Kerner, S. Klenov, D. Wolf, J. Phys. A 35, 9971 (2002)

  49. K. Nagel, M. Schreckenberg, J. Phys. I France 2, 2221 (1992)

  50. M.J. Cassidy, R.L. Bertini, Transportation Research Part B: Methodological 33, 25 (1999)

  51. B. Zielke, R. Bertini, M. Treiber, Empirical Measurement of Freeway Oscillation Characteristics: An International Comparison, Transportation Research Record 2088, 57 (2008)

  52. B.S. Kerner, Physica A 399, 379 (2004)

  53. M. Schönhof, Ph.D. thesis, Technische Universität Dresden (to be published)

  54. B.S. Kerner, in Proc. of the Third International Symposium on Highway Capacity, edited by R. Rysgaard (Road Directorate, Denmark, 1998), Vol. 2, pp. 621–641

  55. M. Treiber, D. Helbing, J. Phys. A 32, L17 (1999)

  56. K. Nishinari, M. Treiber, D. Helbing, Phys. Rev. E 68, 067101 (2003)

  57. B.S. Kerner, Transportation Research Record 1710, 136 (2000)

  58. B. Kerner, Phys. Rev. E 65, 046138 (2002)

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Helbing, D., Treiber, M., Kesting, A. et al. Theoretical vs. empirical classification and prediction of congested traffic states. Eur. Phys. J. B 69, 583–598 (2009). https://doi.org/10.1140/epjb/e2009-00140-5

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PACS

  • 89.40.Bb Land transportation
  • 89.75.Kd Patterns
  • 47.10.ab Conservation laws and constitutive relations