Statistical properties of multiplicative multifractal processes in modelling telecommunications traffic streams

Telecommunications network systems have been observed to contain processing and switching nodes that are loaded by highly bursty traffic streams. Such flows exhibit long-range-dependent (LRD) properties. The design and sizing of electronic processing and switching systems depend critically on the features of such processes. LRD traffic streams are modelled as a multiplicative multifractal process. Through simulation, it is shown that similar queueing performance results can be simultaneously obtained for a network operating at low, medium and high utilisation levels when one compares the system-size tail performance of a single server queueing system driven in the first case by the measured traffic and in the second case by a multiplicative multifractal traffic model. A number of the properties of such processes that are most relevant to their use as network traffic models are proved