Partial balances in batch arrival batch service and assemble-transfer queueing networks

Document Type

Article

Publication Date

1-1-1997

Abstract

Recently Miyazawa and Taylor (1997) proposed a new class of queueing networks with batch arrival batch service and assemble-transfer features. In such networks customers arrive and are served in batches, and may change size when a batch transfers from one node to another. With the assumption of an additional arrival process at each node when it is empty, they obtain a simple product-form steady-state probability distribution, which is a (stochastic) upper bound for the original network. This paper shows that this class of network possesses a set of non-standard partial balance equations, and it is demonstrated that the condition of the additional arrival process introduced by Miyazawa and Taylor is there precisely to satisfy the partial balance equations, i.e. it is necessary and sufficient not only for having a product form solution, but also for the partial balance equations to hold.

Identifier

0031220886 (Scopus)

Publication Title

Journal of Applied Probability

External Full Text Location

https://doi.org/10.1017/S0021900200101391

ISSN

00219002

First Page

745

Last Page

752

Issue

3

Volume

34

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