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 fe atures of such processes. LRD traffic streams are modelled as a multiplicat ive multifractal process. Through simulation, it is shown that similar queu eing performance results can be simultaneously obtained for a network opera ting at low, medium, and high utilisation levels when one compares the syst em-size tail performance of a single server queueing system driven in the f irst case by the measured traffic and in the second case by a multiplicativ e multifractal traffic model. A number of the properties of such processes that are most relevant to their use as network traffic models are proved.