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>α x,Q 2>(1−α)x), for α∈(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.
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Part of this work was done while M.M. was at Stanford University, Stanford, CA 94305, USA.
This research has been funded by the Dutch BSIK/BRICKS (Basic Research in Informatics for Creating the Knowledge Society) project.
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Lieshout, P., Mandjes, M. Asymptotic analysis of Lévy-driven tandem queues. Queueing Syst 60, 203–226 (2008). https://doi.org/10.1007/s11134-008-9094-5
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DOI: https://doi.org/10.1007/s11134-008-9094-5