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May 2004 Exact asymptotics for fluid queues fed by multiple heavy-tailed on–off flows
Bert Zwart, Sem Borst, Michel Mandjes
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Ann. Appl. Probab. 14(2): 903-957 (May 2004). DOI: 10.1214/105051604000000161


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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Bert Zwart. Sem Borst. Michel Mandjes. "Exact asymptotics for fluid queues fed by multiple heavy-tailed on–off flows." Ann. Appl. Probab. 14 (2) 903 - 957, May 2004.


Published: May 2004
First available in Project Euclid: 23 April 2004

zbMATH: 1050.60091
MathSciNet: MR2052908
Digital Object Identifier: 10.1214/105051604000000161

Primary: 60K25
Secondary: 60F10 , 90B22

Keywords: fluid models , heavy-tailed distributions , knapsack problem , large deviations , Queueing theory , reduced-load equivalence

Rights: Copyright © 2004 Institute of Mathematical Statistics


Vol.14 • No. 2 • May 2004
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