The traffic patterns of today's IP networks exhibit two important properties: self-similarity and long-range dependence. The fractional Brownian motion is widely used for representing the traffic model with the properties. We consider a single server fluid queueing system with input process of a fractional Brownian motion type. Packet-loss probability and mean delay are considered as QoS. We show that there is a scaling property among the stationary queue-length distributions of different input parameters and service rates. We also evaluate the scaling factor. From the scaling property, we drive formulas for the effective bandwidth to guarantee the QoS in a single source and multiple sources cases. The formulas indicate that it is essential to evaluate the distribution functions of a type of random variables. For multiple sources the shape of an admissible region and multiplexing gain are analyzed. Finally, numerical examples are shown to validate the proposed scheme. (c) 2004 Elsevier B.V. All rights reserved.