Abstract
We propose a general framework for obtaining asymptotic distributional bounds on the stationary backlog \(W^{A_1 + A_2 ,c} \) 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 ρ1 and r1 , respectively, and with distribution G for the activity periods. The fluid process A 2 of average rate ρ2 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,c>ϰ]∼P[W A1,c—ρ2>ϰ] (ϰ → ∞) holds under the stability condition ρ1 + ρ2 < c and the non-triviality condition c – ρ2 < r 1. In these asymptotics the stationary backlog \({W^{A_1 ,c - \rho _2 } }\) results from feeding source A 1 into a buffer drained at reduced rate c – ρ2. 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.
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Agrawal, R., Makowski, A.M. & Nain, P. On a reduced load equivalence for fluid queues under subexponentiality. Queueing Systems 33, 5–41 (1999). https://doi.org/10.1023/A:1019111809660
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DOI: https://doi.org/10.1023/A:1019111809660