In order to help design and control the emerging high-speed communication networks, we want source traf®c models (also called offered load models or bandwidth demand models) that can be both realistically ®t to data and successfully analyzed. Many recent traf®c measurements have shown that network traf®c is quite complex, exhibiting phenomena such as heavy-tailed probability distributions, longrange dependence, and self similarity; for example, see Caceres et al. [7], Leland  et al. [23], Paxso