Exact Queueing Asymptotics for Multiple Heavy-Tailed On-Off Flows

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. We exploit a powerful intuitive argument to obtain the exact asymptotics for the reduced system. Combined with the reduced-load equivalence, the results for the reduced system provide an asymptotic characterization of the buffer behavior. 2000 Mathematics Subject Classification: 60K25 (primary), 60F10, 90B18, 90B22 (secondary).