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.