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 e [1/2, 1[ is studied. By applying general results on suprema of centred Gaussian processes, in particular, we show that P(V 0 > x) ≤ L/-v e -k2x2(1-H) /2 for large x. Explicit formulae for constants K, y and L are given in terms of H and system parameters.