Lévy-driven GPS queues with heavy-tailed input

Krzysztof Dȩbicki (), Peng Liu (), Michel Mandjes () and Iwona Sierpińska-Tułacz ()
Additional contact information
Krzysztof Dȩbicki: University of Wrocław
Peng Liu: University of Wrocław
Michel Mandjes: University of Amsterdam
Iwona Sierpińska-Tułacz: University of Wrocław

Queueing Systems: Theory and Applications, 2017, vol. 85, issue 3, No 2, 249-267

Abstract: 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 $$\alpha $$ α -stable Lévy motions.

Keywords: Lévy process; Fluid model; Queue; General processor sharing; Exact asymptotics; Primary: 60K25; Secondary: 90B22; 60G51 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11134-016-9510-1 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:queues:v:85:y:2017:i:3:d:10.1007_s11134-016-9510-1

Ordering information: This journal article can be ordered from
http://www.springer.com/journal/11134/

DOI: 10.1007/s11134-016-9510-1

Access Statistics for this article

Queueing Systems: Theory and Applications is currently edited by Sergey Foss

More articles in Queueing Systems: Theory and Applications from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().