The stability condition of BMAP/M/∞ queues

2016/12/20 by Moeko Yajima, Yajima, Moeko, Tuan Phung-Duc +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #math.PR

paper · pdf · doi:10.48550/arxiv.1612.06545

This manuscript is the corrected version of the paper submitted to QTNA2016

arxiv created 2016/12/20 · arxiv updated 2016/12/21

Abstract

This paper considers a BMAP/M/∞ queue with a batch Markovian arrival process (BMAP) and an exponential service time distribution. We first prove that the BMAP/M/∞ 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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