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We study a single-lane traffic model that is based on human driving behavior. The outflow from a traffic jam self-organizes to a critical state of maximum throughput. Small perturbations of the outflow far downstream create emergent traffic jams with a power law distribution P (t) t^-3/2 of lifetimes t. On varying the vehicle density in a closed system, this critical state separates lamellar and jammed regimes and exhibits 1/f noise in the power spectrum. Using random walk arguments, in conjunction with a cascade equation, we develop a phenomenological theory that predicts the critical exponents for this transition and explains the self-organizing behavior. These predictions are consistent with all of our numerical results.
Nagel et al. (Sat,) studied this question.