On a Reduced Load Equivalence for Fluid Queues Under Subexponentiality

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 $\rho_1$ 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 $\bP{W^{A_1+A_2,c}>x} \sim \bP{W^{A_1,c-\rho_2}>x}$ ($x\to\infty$) holds under the stability condition $\rho_1+\rho_2
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RR-3466, INRIA. 1998
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Rajeev Agrawal, Armand M. Makowski, Philippe Nain. On a Reduced Load Equivalence for Fluid Queues Under Subexponentiality. RR-3466, INRIA. 1998. 〈inria-00073224〉

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