SUBEXPONENTIAL ASYMPTOTICS OF THE BMAP/GI/1 QUEUE

Hiroyuki Masuyama; Bin Liu; Tetsuya Takine

doi:10.15807/jorsj.52.377

Journal of the Operations Research Society of Japan

Online ISSN : 2188-8299
Print ISSN : 0453-4514
ISSN-L : 0453-4514

SUBEXPONENTIAL ASYMPTOTICS OF THE BMAP/GI/1 QUEUE

Hiroyuki Masuyama, Bin Liu, Tetsuya Takine

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Keywords: Queue, subexponential asymptotics, independent sampling, BMAP (Batch Markovian Arrival Process), square-root insensitive, random sum

JOURNAL FREE ACCESS

2009 Volume 52 Issue 4 Pages 377-401

DOI https://doi.org/10.15807/jorsj.52.377

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Abstract

This paper considers the stationary queue length and waiting time distributions in a FIFO BMAP/GI/1 queue with heavy-tailed service times and that with heavy-tailed batch sizes. In each case, we provide sufficient conditions under which the stationary queue length and waiting time distributions are subexponential. Furthermore, we obtain asymptotic relationships between the tail distributions of the stationary queue length and waiting time.

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