Jamming transition in the traffic-flow model with two-level crossings.

Abstract

We investigate the effect of two-level crossings on the traffic jam in the cellular-automaton (CA) model of traffic flow. The CA model is an extended version of the traffic-flow model proposed by Biham, Middleton, and Levine [Phys. Rev. A 46, R6124 (1992)]. Its model is described in terms of the CA on the disordered square lattice with two components: one is the site of three states representing the one-level crossing and the other is the site of four states representing the two-level crossing. We find that the dynamical jamming transition does not occur when the fraction c of the two-level crossings becomes larger than the percolation threshold ${\mathit{p}}_{\mathit{p},}$c (cg${\mathit{p}}_{\mathit{p},}$c). The dynamical jamming transition occurs at higher density p of cars with increasing fraction c of the two-level crossings below the percolation threshold (c${\mathit{p}}_{\mathit{p},}$c). We also present a simple mean-field theory for the jamming transition in traffic flow with two-level crossings.