Exact Asymptotics for Fluid Queues Fed by Multiple Heavy-Tailed On-Off Flows

Exact Asymptotics for Fluid Queues Fed by Multiple Heavy-Tailed On-Off Flows

We consider a fluid queue fed by multiple On-Off flows with heavytailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a "dominant" subset of the...

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Veröffentlicht in:The Annals of Applied Probability. - Institute of Mathematical Statistics. - 14(2004), 2, Seite 903-957
1. Verfasser: Zwart, Bert (VerfasserIn)
Weitere Verfasser: Borst, Sem, Mandjes, Michel
Format: Online-Aufsatz
Sprache:English
Veröffentlicht: 2004
Zugriff auf das übergeordnete Werk:The Annals of Applied Probability
Schlagworte:Fluid Models Heavy-Tailed Distributions Knapsack Problem Large Deviations Queueing Theory Reduced-Load Equivalence Business Applied sciences Mathematics Philosophy Behavioral sciences
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520 |a We consider a fluid queue fed by multiple On-Off flows with heavytailed (regularly varying) On periods. Under fairly mild assumptions, we prove that the workload distribution is asymptotically equivalent to that in a reduced system. The reduced system consists of a "dominant" subset of the flows, with the original service rate subtracted by the mean rate of the other flows. We describe how a dominant set may be determined from a simple knapsack formulation. The dominant set consists of a "minimally critical" set of On-Off flows with regularly varying On periods. In case the dominant set contains just a single On-Off flow, the exact asymptotics for the reduced system follow from known results. For the case of several On-Off flows, we exploit a powerful intuitive argument to obtain the exact asymptotics. Combined with the reduced-load equivalence, the results for the reduced system provide a characterization of the tail of the workload distribution for a wide range of traffic scenarios. 
540 |a Copyright 2004 Institute of Mathematical Statistics 
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700 1 |a Mandjes, Michel  |e verfasserin  |4 aut 
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