F → S → F Transitions in Vehicle Probe Data

  • Sven-Eric MolzahnEmail author
  • Boris S. Kerner
  • Hubert Rehborn
  • Sergey L. Klenov
  • Micha Koller
Conference paper


Based on a study of probe vehicle data we have revealed empirical F→S→F transitions before traffic breakdown at the bottleneck theoretically predicted by Kerner. Anonymized probe data from connected vehicles of a large fleet have been collected. The frequency of connected vehicles in our study has been more than ten times larger (on average about 10 s between probe vehicles) than in earlier studies. This data shows that disturbances in free flow evolve in a neighbourhood of the bottleneck leading to small regions of synchronized flow (F→S transition). These regions of synchronized flow dissolve after a random amount of time (traffic recovers to free flow (S→F transition)) before the traffic breakdown occurs. In contrast with the F→S→F transitions, traffic breakdown leads to a long-living congested traffic pattern propagating upstream of the bottleneck. The empirical findings of this paper support some of the theoretical features of the S→F instability.


  1. 1.
    Banks, J.H.: Flow processes at a freeway bottleneck. Transp. Res. Rec. 1297, 20–28 (1990)Google Scholar
  2. 2.
    Chandler, R.E., Herman, R., Montroll, E.W.: Traffic dynamics: studies in car following. Oper. Res. 6(2), 165–184 (1958)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Elefteriadou, L.: An Introduction to Traffic Flow Theory, vol. 84. Springer, New York (2014)CrossRefGoogle Scholar
  4. 4.
    Elefteriadou, L., Roess, R.P., McShane, W.R.: Probabilistic nature of breakdown at freeway merge junctions. Transp. Res. Rec. 1484, 80–89 (1995)Google Scholar
  5. 5.
    Elefteriadou, L., Kondyli, A., Brilon, W., Hall, F.L., Persaud, B., Washburn, S.: Enhancing ramp metering algorithms with the use of probability of breakdown models. J. Transp. Eng. 140(4), 04014003 (2014)CrossRefGoogle Scholar
  6. 6.
    Gartner, N.H., Messer, C.J., Rathi, A.K.: Traffic Flow Theory: A State of the Art Report - Revised Monograph on Traffic Flow Theory. Transportation Research Board, Washington, D.C. (2001)Google Scholar
  7. 7.
    Gazis, D.C., Herman, R., Potts, R.B.: Car-following theory of steady-state traffic flow. Oper. Res. 7(4), 499–505 (1959)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Gazis, D.C., Herman, R., Rothery, R.W.: Nonlinear follow-the-leader models of traffic flow. Oper. Res. 9(4), 545–567 (1961)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Hall, F.L., Agyemang-Duah, K.: Freeway capacity drop and the definition of capacity. Transp. Res. Rec. 1320, 91–98 (1991)Google Scholar
  10. 10.
    Herman, R., Montroll, E.W., Potts, R.B., Rothery, R.W.: Traffic dynamics: analysis of stability in car following. Oper. Res. 7(1), 86–106 (1959)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Kerner, B.S.: The Physics of Traffic. Springer, Berlin (2004)CrossRefGoogle Scholar
  12. 12.
    Kerner, B.S.: Introduction to Modern Traffic Flow Theory and Control: The Long Road to Three-phase Traffic Theory. Springer Science & Business Media, Berlin (2009)CrossRefGoogle Scholar
  13. 13.
    Kerner, B.S.: Microscopic theory of traffic-flow instability governing traffic breakdown at highway bottlenecks: growing wave of increase in speed in synchronized flow. Phys. Rev. E 92(6), 062827 (2015)CrossRefGoogle Scholar
  14. 14.
    Kerner, B.S.: Breakdown in Traffic Networks: Fundamentals of Transportation Science. Springer, Berlin (2017)CrossRefGoogle Scholar
  15. 15.
    Kerner, B.S., Rehborn, H., Schäfer, R.P., Klenov, S.L., Palmer, J., Lorkowski, S., Witte, N.: Traffic dynamics in empirical probe vehicle data studied with three-phase theory: spatiotemporal reconstruction of traffic phases and generation of jam warning messages. Physica A 392(1), 221–251 (2013)CrossRefGoogle Scholar
  16. 16.
    Molzahn, S.E., Kerner, B.S., Rehborn, H., Klenov, S.L., Koller, M.: Analysis of speed disturbances in empirical single vehicle probe data before traffic breakdown. IET Intell. Transp. Syst. 11, 604–612 (2017). CrossRefGoogle Scholar
  17. 17.
    Next generation simulation programs. Accessed 25 Sept 2016

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Sven-Eric Molzahn
    • 1
    Email author
  • Boris S. Kerner
    • 2
  • Hubert Rehborn
    • 1
  • Sergey L. Klenov
    • 3
  • Micha Koller
    • 1
  1. 1.Daimler AG, RD/USN, HPC 059-X901SindelfingenGermany
  2. 2.Physics of Transport and TrafficDuisburgGermany
  3. 3.Moscow Institute of Physics and TechnologyMoscowRussia

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