1 research outputs found
Statistical End-to-end Performance Bounds for Networks under Long Memory FBM Cross Traffic
Fractional Brownian motion (fBm) emerged as a useful model for self-similar
and long-range dependent Internet traffic. Approximate performance measures are
known from large deviations theory for single queuing systems with fBm through
traffic. In this paper we derive end-to-end performance bounds for a through
flow in a network of tandem queues under fBm cross traffic. To this end, we
prove a rigorous sample path envelope for fBm that complements previous
approximate results. We find that both approaches agree in their outcome that
overflow probabilities for fBm traffic have a Weibullian tail. We employ the
sample path envelope and the concept of leftover service curves to model the
remaining service after scheduling fBm cross traffic at a system. Using
composition results for tandem systems from the stochastic network calculus we
derive end-to-end statistical performance bounds for individual flows in
networks under fBm cross traffic. We discover that these bounds grow in O(n
(log n)^(1/(2-2H))) for n systems in series where H is the Hurst parameter of
the fBm cross traffic. We show numerical results on the impact of the
variability and the correlation of fBm traffic on network performance