Subexponential asymptotics of the BMAP/GI/1 queue

Subexponential asymptotics of the BMAP/GI/1 queue

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Article ID: iaor2010216
Volume: 52
Issue: 4
Start Page Number: 377
End Page Number: 401
Publication Date: Dec 2009
Journal: Journal of the Operations Research Society of Japan
Authors: , ,
Keywords: BMAP/G/1 queues
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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