Traffic flow in the Biham-Middleton-Levine model with random update rule.

A stochastic version of the Biham-Middleton-Levine model with random update rule is studied. It is shown that under periodic boundary condition, the system exhibits a sharp transition from moving phase to jamming phase. Under open boundary condition, the coexistence of moving phase and jamming phase can be observed. We have presented a mean-field analysis for the moving phase, which successfully takes into account the correlation and produces good agreement with simulation results.