Non-asymptotic end-to-end performance bounds for networks with long range dependent fBm cross traffic

Fractional Brownian motion (fBm) emerged as a useful model for self-similar and long-range dependent aggregate Internet traffic. Asymptotic, respectively, approximate performance measures are known for single queueing systems with fBm through traffic. In this paper end-to-end performance bounds for a through flow in a network of tandem queues under open-loop fBm cross traffic are derived. To this end, a rigorous sample path envelope for fBm is proven that complements previous approximate results. The sample path envelope and the concept of leftover service curves are employed to model the remaining service after scheduling fBm cross traffic at a queuing system. Using composition results for tandem systems from the stochastic network calculus end-to-end statistical performance bounds for individual flows in networks under fBm cross traffic are derived. The discovery is that these bounds grow in O(n(logn)^1/(2-2H)) for n systems in series where H is the Hurst parameter of the cross traffic. Explicit results on the impact of the variability and the burstiness of through and cross traffic on network performance are shown. Our analysis has direct implications on fundamental questions in network planning and service management.