Open networks of infinite server queues with non-homogeneous multivariate batch Poisson arrivals

Somya Mehra () and Peter G. Taylor
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Somya Mehra: The University of Melbourne
Peter G. Taylor: The University of Melbourne

Queueing Systems: Theory and Applications, 2023, vol. 105, issue 3, No 1, 187 pages

Abstract: 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.

Keywords: Infinite server queue; Open network; Multivariate batch arrivals (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s11134-023-09891-x

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