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.
"Exact asymptotics for fluid queues fed by multiple heavy-tailed on–off flows." Ann. Appl. Probab. 14 (2) 903 - 957, May 2004. https://doi.org/10.1214/105051604000000161