On a Reduced Load Equivalence under Heavy Tail Assumptions

Agrawal, RakeshMakowski, Armand M.Nain, P.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.The equations in this abstract will not display properly unless you have the symbol font installed and your browser supports superscripts and subscripts. Otherwise, you will need to download the paper to see the equations properly.en-USOn/off sourcesFluid queuesLong-range dependenceSubexponential distributionsExtreme value theory,On a Reduced Load Equivalence under Heavy Tail AssumptionsTechnical Report