On a Reduced Load Equivalence under Heavy Tail Assumptions

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We propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog WA1+A2,c in a buffer fed by a combined fluid process A1+A2 and drained at a constant rate c.

The fluid process A1 is an (independent) on-off source with average and peak rates r1 and r1, respectively, and with distribution G for the activity periods. The fluid process A2 of average rate r2 is arbitrary but independent of A1.

These bounds are used to identify subexponential distributions G and fairly general fluid processes A2 such that the asymptotic equivalence P[WA1+A2,c > x]~P[WA1,c-r2 > x](xלּ/font>/font>) holds under the stability condition r1+r2 < c and under the non-triviality condition c-r2 < r1.

The stationary backlog WA1,c-r2in these asymptotics results from feeding source A1 into a buffer drained at reduced rate c-r2. This reduced load asymptotic equivalence extends to a larger class of distributions G a result obtained by Jelenkovic and Lazar [18] in thecase when G belongs to the class of regular intermediatevarying distributions.

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