Sample Path Bounds for Long Memory FBM Traffic

Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent Internet traffic. Asymptotic, respectively, approximate performance measures are known from large deviations theory for single queuing systems with fBm traffic. In this paper we prove a rigorous sample path envelope for fBm that complements previous results. We find that both approaches agree in their outcome that overflow probabilities for fBm traffic have a Weibull tail. We show numerical results on the impact of the variability and the correlation of fBm traffic on the queuing performance.