Self-organized criticality in asymmetric exclusion model with noise for freeway traffic

Abstract

The one-dimensional asymmetric simple-exclusion model with open boundaries for parallel update is extended to take into account temporary stopping of particles. The model presents the traffic flow on a highway with temporary deceleration of cars. Introducing temporary stopping into the asymmetric simple-exclusion model drives the system asymptotically into a steady state exhibiting a self-organized criticality. In the self-organized critical state, start-stop waves (or traffic jams) appear with various sizes (or lifetimes). The typical interval 〈 s〉between consecutive jams scales as 〈 s〉 ≃ L v with v = 0.51 ± 0.05 where L is the system size. It is shown that the cumulative jam-interval distribution N s ( L) satisfies the finite-size scaling form ( N s ( L) ≃ L − v f( s/ L v ). Also, the typical lifetime 〈m7rang; of traffic jams scales as 〈 m〉 ≃ L v ′ with v′ = 0.52 ± 0.05. The cumulative distribution N m ( L) of lifetimes satisfies the finite-size scaling form N m ( L)≃ L −1 g( m/ L v ′).