Tail asymptotics for a Lévy-driven tandem queue with an intermediate input

Tail asymptotics for a Lévy-driven tandem queue with an intermediate input

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Article ID: iaor200973474
Volume: 63
Issue: 1
Start Page Number: 323
End Page Number: 353
Publication Date: Dec 2009
Journal: Queueing Systems
Authors: ,
Keywords: tandem queues
Abstract:

We consider a Lévy-driven tandem queue with an intermediate input assuming that its buffer content process obtained by a reflection mapping has the stationary distribution. For this queue, no closed form formula is known, not only for its distribution but also for the corresponding transform. In this paper, we consider only light-tailed inputs. For the Brownian input case, we derive exact tail asymptotics for the marginal stationary distribution of the second buffer content, while weaker asymptotic results are obtained for the general Lévy input case. The results generalize those of Lieshout and Mandjes from the recent papers (2007 and 2008) for the corresponding tandem queue without an intermediate input.

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