English

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

Probability 2016-12-21 v1

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.

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

R2 v1 2026-06-22T17:29:11.680Z