On a reduced load equivalence for fluid queues under subexponentiality

We propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog W-A1+A2,W-c in a buffer fed by a combined fluid process A(1)+A(2) and drained at a constant rate c. The fluid process A(1) is an (independent) on-off source with average and peak rates rho(1) and r(1), respectively, and with distribution G for the activity periods. The fluid process A(2) of average rate rho(2) is arbitrary but independent of A(1). These bounds are used to identify subexponential distributions G and fairly general fluid processes A(2) such that the asymptotic equivalence P[W-A1+A2,W-c>x]similar to P[W-A1,W-c-rho 2>x] (x --> infinity) holds under the stability condition rho(1)+rho(2)<c and the non-triviality condition c-rho(2)<r(1). In these asymptotics the stationary backlog W-A1,W-c-rho 2 results from feeding source A(1) into a buffer drained at reduced rate c-rho(2). This reduced load asymptotic equivalence extends to a larger class of distributions G a result obtained by Jelenkovic and Lazar [19] in the case when G belongs to the class of regular intermediate varying distributions.