Superposition of multiplicative multifractaltraffic processes

Abstract

Telecommunications network systems have been observed to contain processing and switching nodes that are loaded by highly bursty traffic streams. Such flows have been noted to exhibit long-range-dependent (LRD) properties. The design and sizing of electronic processing and switching systems critically depends on the features of such processes. LRD traffic streams are modelled as a multiplicative multifractal process. It is proven that superposition of a finite number of multiplicative multifractal traffic streams results asymptotically in another multifractal process. Noting that traffic processes driving network nodes result from the superposition of multiple traffic streams at the input ports of the node, this property makes the multiplicative multifractal traffic model a versatile tool for modelling LRD traffic flows at different locations and levels across a network.