Abstract
AbstractIn 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.
Funder
Australian Research Council
Publisher
Springer Science and Business Media LLC
Subject
Computational Theory and Mathematics,Management Science and Operations Research,Computer Science Applications
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