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- Title
Lévy-driven GPS queues with heavy-tailed input.
- Authors
Dȩbicki, Krzysztof; Liu, Peng; Mandjes, Michel; Sierpińska-Tułacz, Iwona
- Abstract
In this paper, we derive exact large buffer asymptotics for a two-class generalized processor sharing (GPS) model, under the assumption that the input traffic streams generated by both classes correspond to heavy-tailed Lévy processes. Four scenarios need to be distinguished, which differ in terms of (i) the level of heavy-tailedness of the driving Lévy processes as well as (ii) the values of the corresponding mean rates relative to the GPS weights. The derived results are illustrated by two important special cases, in which the queues' inputs are modeled by heavy-tailed compound Poisson processes and by $$\alpha $$ -stable Lévy motions.
- Subjects
QUEUEING networks; LEVY processes; POISSON processes; ASYMPTOTIC distribution; MATHEMATICAL models
- Publication
Queueing Systems, 2017, Vol 85, Issue 3/4, p249
- ISSN
0257-0130
- Publication type
Article
- DOI
10.1007/s11134-016-9510-1