The effect of attachment and detachment on totally asymmetric exclusion processes with junctions

In this paper, we investigate totally asymmetric exclusion processes on lattices with junctions, considering random particle attachment and detachment in the bulk. Particles randomly attach to the bulk with the rate omega(A) and detach from the bulk with the rate omega(D). Setting K = omega(A)/omega(D), we study three cases: K > 1, K = 1 and K < 1. Extensive Monte Carlo simulations have been performed. It is found that different phase diagram structures arise in the three cases. While only four stationary phases could be found in the case of K > 1, additional phases are observed in the case of K <= 1. Moreover, it is shown that at a fixed K, the phase diagram structure changes with the increase of omega(D). A mean-field analysis has been carried out and the analytic results are in good agreement with the simulation results.