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Queueing Systems

, Volume 85, Issue 3–4, pp 249–267 | Cite as

Lévy-driven GPS queues with heavy-tailed input

  • Krzysztof Dȩbicki
  • Peng Liu
  • Michel Mandjes
  • Iwona Sierpińska-Tułacz
Article
  • 217 Downloads

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.

Keywords

Lévy process Fluid model Queue General processor sharing Exact asymptotics 

Mathematics Subject Classification

Primary: 60K25 Secondary: 90B22 60G51 

Notes

Acknowledgements

K. Dȩbicki was partially supported by NCN Grant No. 2015/17/B/ST1/01102 (2016-2019), whereas P. Liu was partially supported by the Swiss National Science Foundation Grant 200021-166274. M. Mandjes’ research is partly funded by the NWO Gravitation project Networks, Grant Number 024.002.003. He is also affiliated to (A) CWI, Amsterdam, The Netherlands; (B) Eurandom, Eindhoven University of Technology, Eindhoven, The Netherlands; and (C) Amsterdam Business School, Faculty of Economics and Business, University of Amsterdam, Amsterdam, The Netherlands.

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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Krzysztof Dȩbicki
    • 1
  • Peng Liu
    • 1
    • 2
  • Michel Mandjes
    • 3
  • Iwona Sierpińska-Tułacz
    • 1
  1. 1.Mathematical InstituteUniversity of WrocławWrocławPoland
  2. 2.Department of Actuarial ScienceUniversity of Lausanne, UNIL-DorignyLausanneSwitzerland
  3. 3.Korteweg-de Vries Institute for MathematicsUniversity of AmsterdamAmsterdamThe Netherlands

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