Integrating Fractional Brownian Motion Arrivals into the Statistical Network Calculus

Abstract

Stochastic network calculus (SNC) is a versatile framework to derive probabilistic performance bounds. Recently, it was proposed in [1] to replace the typical a priori assumptions on arrival processes with measurement observations and to incorporate the corresponding statistical uncertainty into calculation of the bounds. This so-called statistical network calculus (StatNC) opens the door for many applications with limited traffic information. However, the important traffic class of self-similar processes such as fractional Brownian Motion (fBm) was left open in [1], thus, e.g., depriving the usage of the StatNC for Internet traffic. In this work, we close this gap by integrating fBm arrivals into the StatNC. To this end, we analyze the impact imposed by the uncertainty on the backlog bound and show in numerical evaluations that the additional inaccuracy is only of moderate size.