Limits of on / off Hierarchical Product Models for Datatransmissionsidney

A hierarchical product model seeks to model network traac as a product of independent on/oo processes. Previous studies have assumed a Markovian structure for component processes amounting to assuming that exponential distributions govern on and oo periods but this is not in good agreement with traac measurements. However, if the number of factor processes grows and input rates are stabilized by allowing the on period distribution to change suitably, a limiting on/of process can be obtained which has exponentially distributed on periods and whose oo periods are equal in distribution to the busy period of an M/G/1 queue. We give a fairly complete study of the possible limits of the product process as the number of factors grow and ooer various characterizations of the approximating processes. We also study the dependence structure of the approximations. 1. Introduction A hierarchical product model seeks to model network traac as a product of independent processes. The idea is that network dynamics depend on various mechanical and software processes and controls which operate at diierent protocol layers and time scales. The consideration of such models is motivated by the need for explanations of both large time scale long range dependence and self-similarity in measured network traac as well as perception of small time scale multifrac-tality. See Kulkarni et al.