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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 adoi:10.1214/105051604000000161 fatcat:7sdrenytvrgczkodrkewmf3igy