Creation and annihilation of traffic jams in a stochastic asymmetric exclusion model with open boundaries: a computer simulation

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Abstract
The creation and annihilation of traffic jams are studied by a computer simulation. The one-dimensional (1D) fully-asymmetric exclusion model with open boundaries for parallel update is extended to take into account stochastic transition of particles (cars) where a particle moves ahead with transition probability pt if the forward nearest neighbour is not occupied. Near pt=1, the system is derived asymptotically into a steady state exhibiting a self-organized criticality. In the self-organized critical state, a traffic jam (start-stop wave) and an empty wave are created at the same time when a car stops temporarily. The traffic jam disappears by colliding with the empty wave. The coalescence process between traffic jams and empty waves is described by the ballistic annihilation process with pair creation. The resulting problem near pt=1 is consistent with the ballistic process in the context of 1D crystal growth studied by Krug and Spohn (1988). The typical lifetime of start-stop waves scales as approximately= Delta pt-0.54+or-0.04 where Delta pt=1-pt. It is shown that the cumulative distribution Nm( Delta pt) of lifetimes satisfies the scaling form Nm( Delta pt) approximately= Delta pt1.1f(m Delta pt0.54). Also, the typical interval between consecutive traffic jams scales as approximately= Delta pt-0.5+or-0.04. The cumulative interval distribution Ns( Delta pt) of traffic jams satisfies the scaling form Ns( Delta pt) approximately= Delta pt0.50g(s Delta pt0.50). For pt<1, no scaling holds.