On a reduced load approximation for a multi-stream fluid model

We propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog W(A₁+A₂ ,c) in a buffer fed by a combined fluid process A₁+A ₂ and drained at a constant rate c. The fluid process A₁ is an (independent) on-off source with average and peak rates ρ₁ and r₁, respectively, and with distribution G for the activity periods. The fluid process A₂ of average rate ρ₂ is arbitrary but independent of Al. These bounds are used to identify subexponential distributions G and fairly general fluid processes A₂ such that the reduced load (asymptotic) equivalence P [W(A₁+A₂,c)>x]~P [W(A₁,c-ρ2)>x] (x→∞) holds under the stability condition ρ₁+ρ₂<c and under the non-triviality condition c-ρ₂<r₁