Effect of unequal injection rates on asymmetric exclusion processes with junction

Abstract

In this paper, we investigate the effect of unequal injection rates on totally asymmetric simple exclusion processes (TASEPs) with a 2-input 1-output junction and parallel update. A mean-field approach is developed to deal with the junction that connects two sub-chains and the single main chain. We obtain the stationary particle currents, density profiles and phase diagrams. Interestingly, we find that the number of stationary-state phases is changeable depending on the value of α1 (α1 is the injection rate on the first sub-chain). When α1 > 1/3, there are seven stationary-state phases in the system, however when α1 < 1/3, only six stationary-state phases exist in the system. The theoretical calculations are shown to be in agreement with Monte Carlo simulations.