To support multimedia applications, high-speed networks must be able to provide quality-of-service (QoS) guarantees for connections with drastically different traf®c characteristics. Some of the characteristics fall beyond the conventional framework of Markov traf®c modeling. For instance, recent studies have demonstrated convincingly that there exists long-range dependence or self-similarity in packet video, which is an important traf®c component in high-speed networks. Essentially, longrange d