Asymptotic analysis of Lévy-driven tandem queues

P.M.D. Lieshout, M.R.H. Mandjes

Research output: Book/ReportReportAcademic

15 Citations (Scopus)

Abstract

We analyze tail asymptotics of a two-node tandem queue with spectrally-positive Lévy input. A first focus lies in the tail probabilities of the type P(Q 1>a x,Q 2>(1-a)x), for a¿(0,1) and x large, and Q i denoting the steady-state workload in the ith queue. In case of light-tailed input, our analysis heavily uses the joint Laplace transform of the stationary buffer contents of the first and second queue; the logarithmic asymptotics can be expressed as the solution to a convex programming problem. In case of heavy-tailed input we rely on sample-path methods to derive the exact asymptotics. Then we specialize in the tail asymptotics of the downstream queue, again in case of both light-tailed and heavy-tailed Lévy inputs. It is also indicated how the results can be extended to tandem queues with more than two nodes.
Original languageEnglish
Place of PublicationAmsterdam
PublisherCentrum voor Wiskunde en Informatica
Number of pages22
Publication statusPublished - 2008

Publication series

NameCWI Report
VolumePNA-R0809

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