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- Title
Asymptotic analysis of Lévy-driven tandem queues.
- Authors
Lieshout, Pascal; Mandjes, Michel
- 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.
- Subjects
ASYMPTOTIC theory of algebraic ideals; LAPLACE transformation; MATHEMATICAL programming; STATISTICAL correlation; CONVEX programming; LOGARITHMIC functions
- Publication
Queueing Systems, 2008, Vol 60, Issue 3/4, p203
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-008-9094-5