  We introduce a model of a totally asymmetric simple exclusion process (TASEP)
on a tree network where the aggregate hopping rate is constant from level to
level. With this choice for hopping rates the model shows the same phase
diagram as the one-dimensional case. The potential applications of our model
are in the area of distribution networks; where a single large source supplies
material to a large number of small sinks via a hierarchical network. We show
that mean field theory (MFT) for our model is identical to that of the
one-dimensional TASEP and that this mean field theory is exact for the TASEP on
a tree in the limit of large branching ratio, $b$(or equivalently large
coordination number). We then present an exact solution for the two level tree
(or star network) that allows the computation of any correlation function and
confirm how mean field results are recovered as $b\rightarrow\infty$. As an
example we compute the steady-state current as a function of branching ratio.
We present simulation results that confirm these results and indicate that the
convergence to MFT with large branching ratio is quite rapid.
