Recent works propose the use of fractional stable noise (FSN) to capture the statistical properties of an arrival process over time intervals. This process can reproduce the properties of long-range dependence and high variability exhibited by traffic in real-life networks. However, when modeling network traffic with this α-stable long-range dependent stochastic process, some analytical difficulties arise. For instance, the value of its index of stability α conditions the existence of some moments, which in turn limits the applicability of traditional statistical procedures. Therefore, alternative procedures and methods have to be used. In this work we claim that in spite of the increased complexity, there is much to gain by considering this modeling approach in the context of traffic control. We focus our attention in the prediction of FSN processes and we argue that it can potentially help improving currently existing resource management mechanisms. We support this claim by introducing the Dynamic Predictive Weighted Fair Queueing; a novel algorithm for the dynamic allocation of resources. Our simulation results and consequent performance comparisons with other schemes suggest that the performance of some scheduling algorithms can be highly improved in terms of packet losses and delays by incorporating prediction techniques that take into account the relevant properties of the network traffic. © 2003 Elsevier Science B.V. All rights reserved.