Asymmetric simple exclusion process on a Cayley tree

We study the asymmetric exclusion process on a regular Cayley tree with arbitrary co-ordination number. In this model particles can enter the system only at the parent site and exit from any of the sites at the last level. In the bulk they move downward to one of the unoccupied neighbours chosen randomly. We show that the steady state current that flows from one level to the next is independent of the exit rate, and increases monotonically with the entry rate and the co-ordination number. Unlike the TASEP, the model has only one phase and the density profile shows no boundary layers.