## The Annals of Applied Probability

### Exact asymptotics for fluid queues fed by multiple heavy-tailed on–off flows

#### 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.

#### Article information

Source
Ann. Appl. Probab., Volume 14, Number 2 (2004), 903-957.

Dates
First available in Project Euclid: 23 April 2004

https://projecteuclid.org/euclid.aoap/1082737117

Digital Object Identifier
doi:10.1214/105051604000000161

Mathematical Reviews number (MathSciNet)
MR2052908

Zentralblatt MATH identifier
1050.60091

#### Citation

Zwart, Bert; Borst, Sem; Mandjes, Michel. Exact asymptotics for fluid queues fed by multiple heavy-tailed on–off flows. Ann. Appl. Probab. 14 (2004), no. 2, 903--957. doi:10.1214/105051604000000161. https://projecteuclid.org/euclid.aoap/1082737117

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