Theoretical investigation of synchronous totally asymmetric exclusion processes on lattices with multiple-input-single-output junctions

摘要

In this paper, we investigate the dynamics of synchronous totally asymmetricexclusion processes on lattices with a multiple-input single-output (MISO)junction, which consists of m subchains for the input and one main chain forthe output. A MISO junction is a type of complex geometry that is relevant tomany biological processes as well as vehicular and pedestrian traffic flow. Amean-field approach is developed to deal with the junction that connects thesubchains and the main chain. Theoretical results for stationary particlecurrents, density profiles, and a phase diagram have been obtained. It is foundthat the phase boundary moves toward the left in the phase diagram with anincrease of the number of subchains. The nonequilibrium stationary states,stationary-state phases, and phase boundaries are determined by the boundaryconditions of the system as well as by the number of subchains. The densityprofiles obtained from computer simulations show very good agreement with ourtheoretical analysis.