Large buffer asymptotics for the queue with fractional Brownian input

Abstract

In this paper, a strong asymptotic estimate for the queue content distribution of a fluid queue fed by a fractional Brownian input with Hurst parameter H ∊ [1/2,1[is studied. By applying general results on suprema of centred Gaussian processes, in particular, we show that for large x. Explicit formulae for constants κ, γ and L are given in terms of H and system parameters.