  In this paper, we consider the occupancy distribution for an open network of
infinite server queues with multivariate batch arrivals following a
non-homogeneous Poisson process, and general service time distributions. We
derive a probability generating function for the transient occupancy
distribution of the network, and prove that it is necessary and sufficient for
ergodicity that the expected occupancy time for each batch be finite. Further,
we recover recurrence relations for the transient probability mass function
formulated in terms of a distribution obtained by compounding the batch size
with a multinomial distribution.
