Self-Organized Criticality and $1/f$ Noise in Traffic

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Paczuski, Maya ; Nagel, Kai (1996)
  • Subject: Condensed Matter | Nonlinear Sciences - Adaptation and Self-Organizing Systems

Phantom traffic jams may emerge ``out of nowhere'' from small fluctuations rather than being triggered by large, exceptional events. We show how phantom jams arise in a model of single lane highway traffic, which mimics human driving behavior. Surprisingly, the optimal state of highest efficiency, with the largest throughput, is a critical state with traffic jams of all sizes. We demonstrate that open systems self-organize to the most efficient state. In the model we study, this critical state is a percolation transition for the phantom traffic jams. At criticality, the individual jams have a complicated fractal structure where cars follow an intermittent stop and go pattern. We analytically derive the form of the corresponding power spectrum to be $1/f^{\alpha}$ with $\alpha =1$ exactly. This theoretical prediction agrees with our numerical simulations and with observations of $1/f$ noise in real traffic.
  • References (16)
    16 references, page 1 of 2

    1. K. Nagel and M. Paczuski, Phys. Rev. E 51, 2909 (1995).

    2. S. Maslov, M. Paczuski, and P. Bak, Phys. Rev. Lett. 73, 2162 (1994).

    3. M. Paczuski, S. Maslov, and P. Bak, Phys. Rev. E (in press).

    4. T. Musha and H. Higuchi, Jap. J. Appl. Phys. 15, 1271 (1976); ibid 17, 811 (1978).

    5. H. Herrmann's article in the same volume.

    6. F.L. Hall, B.L. Allen, and M.A. Gunter, Trans. Res. A 20, 197 (1986); see Hall's article in the same volume.

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

    8. K. Nagel, Int. J. Mod. Phys. C 5, 567 (1994).

    9. W. Feller, An Introduction to Probability Theory and Its Applications, Vol. 1 (Wiley, New York 1968).

    10. Note that for vmax = 1 the jams do not branch, and 1/f noise is not observed.

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