Asymmetric exclusion processes on mm-input nn-output junctions with parallel update

In this paper, we investigate totally asymmetric exclusion processes (TASEPs) on lattices with an mm-input nn-output junction in parallel update. A general theoretical solution for traffic dynamics of TASEPs with a junction is developed. More interestingly, mm-input nn-output junctions can be classified by a parameter, λ=m/nλ=m/n. The junctions with the same λλ exhibit the same dynamic properties (e.g., phase diagrams, stationary currents, and density profiles). When the number of mm and/or nn changes, the low-density and high-density regions can be measured qualitatively and quantitatively. The phase diagram is obtained from a simple mean-field approximation and supported by computer simulations. Stationary current and density profiles are calculated which show good agreement with computer simulations.