  Totally asymmetric simple exclusion processes, consisting of two coupled
parallel lattice chains with particles interacting with hard-core exclusion and
moving along the channels and between them, are considered. In the limit of
strong coupling between the channels, the particle currents, density profiles
and a phase diagram are calculated exactly by mapping the system into an
effective one-channel totally asymmetric exclusion model. For intermediate
couplings, a simple approximate theory, that describes the particle dynamics in
vertical clusters of two corresponding parallel sites exactly and neglects the
correlations between different vertical clusters, is developed. It is found
that, similarly to the case of one-channel totally asymmetric simple exclusion
processes, there are three stationary state phases, although the phase
boundaries and stationary properties strongly depend on inter-channel coupling.
An extensive computer Monte Carlo simulations fully support the theoretical
predictions.
