Theoretical investigation of asymmetric exclusion processes on m-input n-output junctions with random update

In this paper, we investigate totally asymmetric exclusion processes (TASEPs) on lattices with an m-input n-output junction in random update. A general theoretical solution for traffic dynamics of TASEPs with a junction is developed. The model is reminiscent of biological transport and vehicular transport. When the number of m and/or n 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.