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Asymptotics of Hybrid Fluid Queues with Lévy Input

Part of: Limit theorems Special processes Stochastic processes

Published online by Cambridge University Press:  30 January 2018

Krzysztof Dębicki ,
Iwona Sierpińska  and
Bert Zwart
Krzysztof Dębicki*
Affiliation:
University of Wrocław
Iwona Sierpińska*
Affiliation:
University of Wrocław
Bert Zwart*
Affiliation:
CWI, VU University Amsterdam, EURANDOM, and Georgia Institute of Technology
*
∗ Postal address: Instytut Matematyczyny, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
∗ Postal address: Instytut Matematyczyny, University of Wrocław, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
∗∗∗∗ Email address: bert.zwart@cwi.nl
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Abstract

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Let {X(t):t∈ℝ} be the integrated on–off process with regularly varying on-periods, and let {Y(t):t∈ℝ} be a centered Lévy process with regularly varying positive jumps (independent of X(·)). We study the exact asymptotics of ℙ(supt≥0{X(t)+Y(t)-ct}>u) as u→∞, with special attention to the case r=c, where r is the increase rate of the on–off process during the on-periods.

Keywords

Exact asymptoticsLévy processfluid modelqueue

MSC classification

Primary: 60G15: Gaussian processes
Secondary: 60G70: Extreme value theory; extremal processes 60F10: Large deviations 60K25: Queueing theory
Type
Research Article
Information
Journal of Applied Probability , Volume 50 , Issue 1 , March 2013 , pp. 103 - 113
Copyright
Copyright © Applied Probability Trust 2013 

Footnotes

Supported by MNiSW grant N N2014079 33 (2007–2009) and by a Marie Curie Transfer of Knowledge Fellowship of the European Community's Sixth Framework Programme under contract MTKD-CT-2004-013389.

Partly supported by NSF grants 0727400 and 0805979, an IBM facility award, and a VIDI grant from NWO.

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