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 (to) 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 drived 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. The typical lifetime (rn) of start-stop waves scales as [m] approximate to Delta p(t)(-0.5410.04) 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)) approximate to Delta p(t)(1.1) f(m Delta p(t)(0.54)). Also, the typical interval [s] between consecutive traffic jams scales as [s] approximate to Delta p(t)(-0.50+/-0.04). The cumulative interval distribution N-s(Delta p(t)) of traffic jams satisfies the scaling form N-s(Delta p(t)) approximate to Delta p(t)(0.50)g(s Delta p(t)(0.50)). For p(t) < 1, no scaling holds.