  We introduce a multi-species lattice gas model for motor protein driven
collective cargo transport on cellular filaments. We use this model to describe
and analyze the collective motion of interacting vesicle cargoes being carried
by oppositely directed molecular motors, moving on a single biofilament.
Building on a totally asymmetric exclusion process (TASEP) to characterize the
motion of the interacting cargoes, we allow for mass exchange with the
environment, input and output at filament boundaries and focus on the role of
interconversion rates and how they affect the directionality of the net cargo
transport. We quantify the effect of the various different competing processes
in terms of non-equilibrium phase diagrams. The interplay of interconversion
rates, which allow for flux reversal and evaporation/deposition processes
introduce qualitatively new features in the phase diagrams. We observe regimes
of three-phase coexistence, the possibility of phase re-entrance and a
significant flexibility in how the different phase boundaries shift in response
to changes in control parameters. The moving steady state solutions of this
model allows for different possibilities for the spatial distribution of cargo
vesicles, ranging from homogeneous distribution of vesicles to polarized
distributions, characterized by inhomogeneities or {\it shocks}. Current
reversals due to internal regulation emerge naturally within the framework of
this model. We believe this minimal model will clarify the understanding of
many features of collective vesicle transport, apart from serving as the basis
for building more exact quantitative models for vesicle transport relevant to
various {\it in-vivo} situations.
