Large buffer asymptotics for the queue with fractional Brownian input

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 P(V0 > x) ≤ L/x^γ e^{–κ2x2(1–H)/2} for large x. Explicit formulae for constants κ, γ and L are given in terms of H and system parameters.