Annals of Applied Probability

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

Bert Zwart, Sem Borst, and Michel Mandjes

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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

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

First available in Project Euclid: 23 April 2004

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60K25: Queueing theory [See also 68M20, 90B22]
Secondary: 60F10: Large deviations 90B22: Queues and service [See also 60K25, 68M20]

Fluid models heavy-tailed distributions knapsack problem large deviations queueing theory reduced-load equivalence


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.

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