Self-organized criticality and 1/f noise in traffic

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{sup {alpha}} with {alpha} = 1 exactly. This theoretical prediction agrees with our numerical simulations and with observations of 1/f noise in real traffic