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arXiv · 1612.06545

The stability condition of BMAP/M/$\infty$ queues

Moeko Yajima·Tuan Phung-Duc·Hiroyuki Masuyama
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Abstract

This paper considers a BMAP/M/$\infty$ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/$\infty$ queue is stable if and only if the expectation of the logarithm of the batch-size distribution is finite. Using this result, we also present the stability condition for an infinite-server queue with a multiclass batch Markovian arrival process and class-dependent exponential service times.

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Moeko Yajima, Tuan Phung-Duc, Hiroyuki Masuyama. 2016-12-20. The stability condition of BMAP/M/$\infty$ queues. https://arxiv.org/abs/1612.06545

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