Disordered cellular automaton traffic flow model: Phase separated state, density waves and self organized criticality

We suggest a disordered traffic flow model that captures many features of traffic flow. It is an extension of the Nagel-Schreckenberg (NaSch) stochastic cellular automata for single line vehicular traffic model. It incorporates random acceleration and deceleration terms that may be greater than one unit. Our model leads under its intrinsic dynamics, for high values of braking probability $p$, to a constant flow at intermediate densities without introducing any spatial inhomogeneities. For a system of fast drivers $p\to 0$, the model exhibits a density wave behavior that was observed in car following models with optimal velocity. The gap of the disordered model we present exhibits, for high values of $p$ and random deceleration, at a critical density, a power law distribution which is a hall mark of a self organized criticality phenomena.