We propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog in a buffer fed by a combined fluid process and drained at a constant rate c. The fluid process A1 is an (independent) on–off source with known average and peak rates and with distribution G for the activity periods. The fluid process A2 is arbitrary but independent of A1. Bounds are used to identify subexponential distributions G and fairly general fluid processes A2 such that an asymptotic equivalence holds under the stability non-triviality conditions. In these asymptotics the stationary backlog results from feeding source A1 into a buffer drained at reduced rate. This reduced load asymptotic equivalence extends to a larger class of distributions G, a result obtained by Jelenkovic and Lazar in the case when G belongs to the class of regular intermediate varying distributions.
