Variance-Driven Traffic Dynamics

  • Martin Treiber
  • Arne Kesting
  • Dirk Helbing
Conference paper

Summary

We investigate the adaptation of the time headways in car-following models as a function of the local velocity variance, which is a measure of the inhomogeneity of traffic flows. We apply our meta-model to several car-following models and simulate traffic breakdowns in open systems with an on-ramp bottleneck. Single-vehicle data generated by ‘virtual detectors’ show a semi-quantitative agreement with microscopic data from the Dutch freeway A9. This includes the observed distributions of the net time headways and times-to-collisions for free and congested traffic, and the velocity variance as a function of traffic density. Macroscopic properties such as the observed wide scattering of flow-density data are reproduced as well, even for deterministic simulations. We explain these phenomena by a self-organized variance-driven process that leads to the spontaneous formation and decay of long-lived platoons.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Helbing, “Traffic and related self-driven many-particle systems,” Rev. Mod. Phys. 73, 1067–1141 (2001).CrossRefGoogle Scholar
  2. 2.
    B. S. Kerner, The Physics of Traffic (Springer, Heidelberg, 2004).Google Scholar
  3. 3.
    K. Nishinari, M. Treiber, and D. Helbing, “Interpreting the wide scattering of synchronized traffic data by time gap statistics,” Phys. Rev. E 68, 067101 (2003).CrossRefGoogle Scholar
  4. 4.
    M. Treiber, A. Hennecke, and D. Helbing, “Derivation, properties, and simulation of a gas-kinetic-based, non-local traffic model,” Phys. Rev. E 59, 239–253 (1999).CrossRefGoogle Scholar
  5. 5.
    M. Bando, K. Hasebe, A. Nakayama, A. Shibata, and Y. Sugiyama, “Dynamical model of traffic congestion and numerical simulation,” Phys. Rev. E 51, 1035–1042 (1995).CrossRefGoogle Scholar
  6. 6.
    R. Jiang, Q. Wu, and Z. Zhu, “Full velocity difference model for a car-following theory,” Phys. Rev. E 64, 017101 (2001).CrossRefGoogle Scholar
  7. 7.
    M. Treiber, A. Hennecke, and D. Helbing, “Congested traffic states in empirical observations and microscopic simulations,” Phys. Rev. E 62, 1805–1824 (2000).CrossRefGoogle Scholar
  8. 8.
    P. G. Gipps, “A behavioural car-following model for computer simulation,” Transp. Res. B 15, 105–111 (1981).CrossRefGoogle Scholar
  9. 9.
    M. Treiber, A. Kesting, and D. Helbing, “Delays, inaccuracies and anticipation in microscopic traffic models,” Physica A 359, 729–746 (2006).Google Scholar
  10. 10.
    D. Helbing and M. Treiber, “Fokker-Planck equation approach to vehicle statistics,” (2003), cond-mat/0307219.Google Scholar
  11. 11.
    M. Treiber, A. Kesting, and D. Helbing, “Understanding widely scattered traffic flows, the capacity drop, platoons, and times-to-collision as effects of variance-driven time gaps,” preprint physics/0508222 (2005).Google Scholar
  12. 12.
    A. Kesting, M. Treiber, M. Schönhof, F. Kranke, and D. Helbing, “‘Jamavoiding’ adaptive cruise control (ACC) and its impact on traffic dynamics”, these proceedings.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Martin Treiber
    • 1
  • Arne Kesting
    • 1
  • Dirk Helbing
    • 1
    • 2
  1. 1.Institute for Transport & EconomicsTechnische Universität DresdenDresdenGermany
  2. 2.Collegium Budapest — Institute for Advanced StudyBudapestHungary

Personalised recommendations