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

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 p_t if the forward nearest neighbour is not occupied. Near p_t=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 p_t=1 is consistent with the ballistic process in the context of 1D crystal growth studied by Krug and Spohn (1988). The typical lifetime <m> of start-stop waves scales as <m> approximately= Delta p_t^{-0.54+or-0.04} where Delta p_t=1-p_t. It is shown that the cumulative distribution N_m( Delta p_t) of lifetimes satisfies the scaling form N_m( Delta p_t) approximately= Delta p_t^1.1f(m Delta p_t^0.54). Also, the typical interval <s> between consecutive traffic jams scales as <s> approximately= Delta p_t^-0.5+or-0.04. The cumulative interval distribution N_s( Delta p_t) of traffic jams satisfies the scaling form N_s( Delta p_t) approximately= Delta p_t^0.50g(s Delta p_t^0.50). For p_t<1, no scaling holds.