Theoretical vs. Empirical Classification and Prediction of Congested Traffic States

  • Dirk Helbing
  • Martin Treiber
  • Arne Kesting
  • Martin Schönhof
Part of the Lecture Notes in Mathematics book series (LNM, volume 2062)


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.


Traffic Flow Traffic State Congested Traffic Traffic Model Fundamental Diagram 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



DH and MT are grateful for the inspiring discussions with the participants of the Workshop on “Multiscale Problems and Models in Traffic Flow” organized by Michel Rascle and Christian Schmeiser at the Wolfgang Pauli Institute in Vienna from May 5–9, 2008, with partial support by the CNRS. Furthermore, the authors would like to thank for financial support by the Volkswagen AG within the BMBF research initiative INVENT and the Hessisches Landesamt für Straßen und Verkehrswesen for providing the freeway data.


  1. 1.
    P.F. Arndt, Phys. Rev. Lett. 84, 814 (2000)CrossRefGoogle Scholar
  2. 2.
    M. Bando, K. Hasebe, K. Nakanishi, A. Nakayama, Phys. Rev. E 58, 5429 (1998)CrossRefGoogle Scholar
  3. 3.
    R. Barlovic, T. Huisinga, A. Schadschneider, M. Schreckenberg, Phys. Rev. E 66(4), 046113 (2002)CrossRefGoogle Scholar
  4. 4.
    E. Brockfeld, R.D. Kühne, A. Skabardonis, P. Wagner, Transp. Res. Rec. 1852, 124 (2003)CrossRefGoogle Scholar
  5. 5.
    E. Brockfeld, R.D. Kühne, P. Wagner, Transp. Res. Rec. 1876, 62 (2004)CrossRefGoogle Scholar
  6. 6.
    M.J. Cassidy, R.L. Bertini, Transp. Res. B Methodol. 33, 25 (1999)CrossRefGoogle Scholar
  7. 7.
    M. Evans, Y. Kafri, H. Koduvely, D. Mukamel, Phys. Rev. Lett. 80, 425 (1998)CrossRefGoogle Scholar
  8. 8.
    D. Helbing, Rev. Mod. Phys. 73, 1067 (2001)CrossRefGoogle Scholar
  9. 9.
    D. Helbing, J. Phys. A 36(46), L593 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    D. Helbing, M. Moussaid, Eur. Phys. J. B 69, 571–581 (2009)CrossRefGoogle Scholar
  11. 11.
    D. Helbing, B. Tilch, Phys. Rev. E 58, 133 (1998)CrossRefGoogle Scholar
  12. 12.
    D. Helbing, B. Tilch, Eur. Phys. J. B 68, 577–586 (2009)zbMATHCrossRefGoogle Scholar
  13. 13.
    D. Helbing, A. Hennecke, M. Treiber, Phys. Rev. Lett. 82, 4360 (1999)CrossRefGoogle Scholar
  14. 14.
    D. Helbing, A. Hennecke, V. Shvetsov, M. Treiber, Math. Comput. Model. 35, 517 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    R. Jiang, Q. Wu, B. Wang, Phys. Rev. E 66(3), 36104 (2002)CrossRefGoogle Scholar
  16. 16.
    B.S. Kerner, in Proceedings of the Third International Symposium on Highway Capacity, vol. 2, ed. by R. Rysgaard (Road Directorate, Denmark, 1998), pp. 621–641Google Scholar
  17. 17.
    B. Kerner, Phys. Rev. Lett. 81(17), 3797 (1998)zbMATHCrossRefGoogle Scholar
  18. 18.
    B.S. Kerner, Transp. Res. Rec. 1710, 136 (2000)CrossRefGoogle Scholar
  19. 19.
    B. Kerner, Phys. Rev. E 65, 046138 (2002)CrossRefGoogle Scholar
  20. 20.
    B.S. Kerner, The Physics of Traffic (Springer, Heidelberg, 2004)CrossRefGoogle Scholar
  21. 21.
    B.S. Kerner, Phys. A 399, 379 (2004)MathSciNetGoogle Scholar
  22. 22.
    B. Kerner, S. Klenov, J. Phys. A 35, L31 (2002)zbMATHGoogle Scholar
  23. 23.
    B. Kerner, S. Klenov, J. Phys. A Math. Gen. 35, L31 (2002)zbMATHCrossRefGoogle Scholar
  24. 24.
    B. Kerner, P. Konhäuser, Phys. Rev. E 48(4), 2335 (1993)CrossRefGoogle Scholar
  25. 25.
    B. Kerner, H. Rehborn, Phys. Rev. E 53, R1297 (1996)CrossRefGoogle Scholar
  26. 26.
    B. Kerner, H. Rehborn, Phys. Rev. E 53, R4275 (1996)CrossRefGoogle Scholar
  27. 27.
    B. Kerner, H. Rehborn, Phys. Rev. Lett. 79, 4030 (1997)CrossRefGoogle Scholar
  28. 28.
    B. Kerner, S. Klenov, D. Wolf, J. Phys. A 35(47), 9971 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  29. 29.
    A. Kesting, M. Treiber, Transp. Res. Rec. 2088, 148 (2008)CrossRefGoogle Scholar
  30. 30.
    A. Kesting, M. Treiber, D. Helbing, Transp. Res. Rec. 1999, 86 (2007)CrossRefGoogle Scholar
  31. 31.
    A. Kesting, M. Treiber, M. Schönhof, D. Helbing, Transp. Res. C Emerg. Tech. 16(6), 668 (2008)CrossRefGoogle Scholar
  32. 32.
    J. Krug, Phys. Rev. Lett. 67, 1882 (1991)MathSciNetCrossRefGoogle Scholar
  33. 33.
    R. Kubo, Rep. Prog. Phys. 29, 255 (1966)CrossRefGoogle Scholar
  34. 34.
    H. Lee, H. Lee, D. Kim, Phys. Rev. Lett. 81, 1130 (1998)CrossRefGoogle Scholar
  35. 35.
    H.Y. Lee, H.W. Lee, D. Kim, Phys. Rev. E 59, 5101 (1999)CrossRefGoogle Scholar
  36. 36.
    H. Lee, H. Lee, D. Kim, Phys. Rev. E 62, 4737 (2000)CrossRefGoogle Scholar
  37. 37.
    M. Lighthill, G. Whitham, Proc. R. Soc. Lond. A 229, 317 (1955)MathSciNetzbMATHCrossRefGoogle Scholar
  38. 38.
    S. Lübeck, M. Schreckenberg, K.D. Usadel, Phys. Rev. E 57, 1171 (1998)CrossRefGoogle Scholar
  39. 39.
    K. Nagel, M. Schreckenberg, J. Phys. I Fr. 2, 2221 (1992)CrossRefGoogle Scholar
  40. 40.
    K. Nishinari, M. Treiber, D. Helbing, Phys. Rev. E 68, 067101 (2003)CrossRefGoogle Scholar
  41. 41.
    S. Ossen, S.P. Hoogendoorn, Transp. Res. Rec. 1934, 13 (2005)CrossRefGoogle Scholar
  42. 42.
    S. Ossen, S.P. Hoogendoorn, B.G. Gorte, Transp. Res. Rec. 1965, 121 (2007)CrossRefGoogle Scholar
  43. 43.
    V. Popkov, L. Santen, A. Schadschneider, G.M. Schütz, J. Phys. A Math. Gen. 34, L45 (2001)zbMATHCrossRefGoogle Scholar
  44. 44.
    M. Schönhof, D. Helbing, Transp. Sci. 41, 1 (2007)CrossRefGoogle Scholar
  45. 45.
    M. Schönhof, Ph.D. thesis, Technische Universität Dresden (Unpublished)Google Scholar
  46. 46.
    G. Schütz, E. Domany, J. Stat. Phys. 72, 277 (1993)zbMATHGoogle Scholar
  47. 47.
    F. Siebel, W. Mauser, Phys. Rev. E 73(6), 66108 (2006)MathSciNetCrossRefGoogle Scholar
  48. 48.
    Y. Sugiyama, M. Fukui, M. Kikuchi, K. Hasebe, A. Nakayama, K. Nishinari, S. Tadaki, S. Yukawa, New J. Phys. 10, 033001 (2008)CrossRefGoogle Scholar
  49. 49.
    M. Treiber, D. Helbing, J. Phys. A 32(1), L17 (1999)CrossRefGoogle Scholar
  50. 50.
    M. Treiber, D. Helbing, Coop. Transp. Dyn. 1, 3.1 (2002). Internet Journal, see
  51. 51.
    M. Treiber, D. Helbing, Eur. Phys. J. B 68, 607–618 (2009)CrossRefGoogle Scholar
  52. 52.
    M. Treiber, A. Hennecke, D. Helbing, Phys. Rev. E 59, 239 (1999)CrossRefGoogle Scholar
  53. 53.
    M. Treiber, A. Hennecke, D. Helbing, Phys. Rev. E 62, 1805 (2000)CrossRefGoogle Scholar
  54. 54.
    M. Treiber, A. Kesting, D. Helbing, Phys. A 360, 71 (2006)CrossRefGoogle Scholar
  55. 55.
    M. Treiber, A. Kesting, D. Helbing, Three-phase traffic theory and two-phase models with a fundamental diagram in the light of empirical stylized facts. Transport. Res. B Methodological 44(8–9), 983–1000 (2010)CrossRefGoogle Scholar
  56. 56.
    J. Treiterer, J. Myers, in Proceedings of the 6th International Symposium on Transportation and Traffic Theory, ed. by D. Buckley (Elsevier, New York, 1974), p. 13Google Scholar
  57. 57.
    G.B. Whitham, Linear and Nonlinear Waves (Wiley-Interscience, New York, 1974)zbMATHGoogle Scholar
  58. 58.
    B. Zielke, R. Bertini, M. Treiber, Empirical Measurement of Freeway Oscillation Characteristics: An International Comparison. Transportation Research Board Annual Meeting, Paper #08-0300, 2008Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Dirk Helbing
    • 1
  • Martin Treiber
    • 2
  • Arne Kesting
    • 2
  • Martin Schönhof
    • 2
  1. 1.ETH Zurich, UNO D11Universitätstr. 41ZurichSwitzerland
  2. 2.Institute for Transport & EconomicsDresden University of TechnologyDresdenGermany

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