Theoretical investigation of synchronous totally asymmetric simple exclusion process on lattices with two consecutive junctions in multiple-input-multiple-output traffic system

In this paper, we study the dynamics of the synchronous totally asymmetric simple exclusion process (TASEP) on lattices with two consecutive junctions in a multiple-input-multiple-output (MIMO) traffic system, which consists of m sub-chains for the input and the output, respectively. In the middle of the system, there are n (n < m) sub-chains via two consecutive junctions linking m sub-chains of input and m sub-chains of output, respectively. This configuration is a type of complex geometry that is relevant to many biological processes as well as to vehicular traffic flow. We use a mean-field approach to calculate this typical geometry and obtain the theoretical results for stationary particle currents, density profiles, and a phase diagram. With the values of m and n synchronously increasing, the vertical phase boundary moves toward the right and the horizontal phase boundary moves toward the upside in the phase diagram. The boundary conditions of the system as well as the numbers of input and output determine the no-equilibrium stationary states, stationary-states phases, and phase boundaries. We use the results to compare with computer simulations and find that they are in very good agreement with each other.