Effect of unequal injection rates on asymmetric exclusion processes with junction

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 \alpha_1 (\alpha_1 is the injection rate on the first sub-chain). When \alpha_1 > 1/3, there are seven stationary-state phases in the system, however when \alpha_1 < 1/3, only six stationary-state phases exist in the system. The theoretical calculations are shown to be in agreement with Monte Carlo simulations.