Exact asymptotics for fluid queues fed by multiple heavy-tailed on–off flows
Bert Zwart, Sem Borst, and Michel Mandjes
Source: Ann. Appl. Probab. Volume 14, Number 2
(2004), 903-957.
Abstract
We consider a fluid queue fed by multiple On–Off flows with heavy-tailed (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.
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Keywords: Fluid models; heavy-tailed distributions; knapsack problem; large deviations; queueing theory; reduced-load equivalence
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Permanent link to this document: http://projecteuclid.org/euclid.aoap/1082737117
Digital Object Identifier: doi:10.1214/105051604000000161
Mathematical Reviews number (MathSciNet): MR2052908
Zentralblatt MATH identifier: 1050.60091
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