Tail asymptotics for the busy period in the G1/G/1 queue

Tail asymptotics for the busy period in the G1/G/1 queue

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Article ID: iaor20041261
Country: United States
Volume: 26
Issue: 3
Start Page Number: 485
End Page Number: 493
Publication Date: Aug 2001
Journal: Mathematics of Operations Research
Authors:
Keywords: GI/G/1 queues
Abstract:

We characterise the tail behaviour of the busy period distribution in the GI/G/1 queue under the assumption that the tail of the service time distribution is of intermediate regular variation. This extends a result of de Meyer and Teugels, who treated the M/G/1 queue with a regularly varying service time distribution. Our method of proof is, opposed to the one in de Meyer and Teugels, probabilistic, and reveals an insightful relationship between the busy period and the cycle maximum.

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