Theoretical investigation of totally asymmetric exclusion processes on lattices with junctions

Totally asymmetric simple exclusion processes on lattices with junctions, where particles interact with hard core exclusion and move on parallel lattice branches that at the junction combine into a single lattice segment, are investigated. A simple approximate theory, that treats the correlations around the junction position in a mean-field fashion, is developed in order to calculate stationary particle currents, density profiles and a phase diagram. It is shown that there are three possible stationary phases depending on the state of each of the lattice branches. At first-order phase boundaries, where the density correlations are important, a modified phenomenological domain wall theory, that accounts for correlations, is introduced. Extensive Monte Carlo computer simulations are performed to investigate the system, and it is found that they are in excellent agreement with theoretical predictions. The application of the theoretical method for other inhomogeneous asymmetric simple exclusion processes is outlined.