The stability condition of BMAP/M/$\infty$ queues
Probability
2016-12-21 v1
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.
Keywords
Cite
@article{arxiv.1612.06545,
title = {The stability condition of BMAP/M/$\infty$ queues},
author = {Moeko Yajima and Tuan Phung-Duc and Hiroyuki Masuyama},
journal= {arXiv preprint arXiv:1612.06545},
year = {2016}
}
Comments
This manuscript is the corrected version of the paper submitted to QTNA2016