  In this paper, we investigate the dynamics of synchronous totally asymmetric
exclusion processes on lattices with a multiple-input single-output (MISO)
junction, which consists of m subchains for the input and one main chain for
the output. A MISO junction is a type of complex geometry that is relevant to
many biological processes as well as vehicular and pedestrian traffic flow. A
mean-field approach is developed to deal with the junction that connects the
subchains and the main chain. Theoretical results for stationary particle
currents, density profiles, and a phase diagram have been obtained. It is found
that the phase boundary moves toward the left in the phase diagram with an
increase of the number of subchains. The nonequilibrium stationary states,
stationary-state phases, and phase boundaries are determined by the boundary
conditions of the system as well as by the number of subchains. The density
profiles obtained from computer simulations show very good agreement with our
theoretical analysis.
