This paper introduces the computation of delay and backlog bounds for a generalized processor sharing (GPS) server under long-range dependent (LRD) traffic. The traffic is supposed to be regulated by the Fractal Leaky Bucket policing mechanism, which is an appropriate regulator for LRD traffic. Results are extended to a network of GPS servers with arbitrary topology, and the stability of those networks is analysed. (C) 2002 Elsevier Science B.V. All rights reserved.