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

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

1996-02-02

arxiv.org/abs/cond-mat/9602011v1

Physics

Condensed Matter

13 pages, uuencoded with style file mprocl.sty. 6 Figures not included but can be mailed on request. Will appear in ``Traffic

Scientific paper

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.

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