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- Title
Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals.
- Authors
Mehra, Somya; Taylor, Peter G.
- Abstract
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.
- Subjects
QUEUING theory; MULTINOMIAL distribution; POISSON processes; QUEUEING networks; GENERATING functions; PROBABILITY theory
- Publication
Queueing Systems, 2023, Vol 105, Issue 3/4, p171
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-023-09891-x