Multiplicative multifractal modelling of long-range-dependent network traffic

We present a multiplicative multifractal process to model tra$c which exhibits long-range dependence. Using tra$c trace data captured by Bellcore from operations across local and wide area networks, we examine the interarrival time series and the packet length sequences.We also model the frame size sequences of VBR video tra$c process. We prove a number of properties of multiplicative multifractal processes that are most relevant to their use as tra$c models. In particular, we show these processes to characterize e!ectively the long-range dependence properties of the measured processes. Furthermore, we consider a single server queueing system which is loaded, on one hand, by the measured processes, and, on the other hand, by our multifractal processes (the latter forming a MF /MF /1 queueing system model). In comparing the performance of both systems, we demonstrate our models to e!ectively track the behaviour exhibited by the system driven by the actual tra$c processes. We show the multiplicative multifractal process to be easy to construct. Through parametric dependence on one or two parameters, this model can be calibrated to "t the measured data. We also show that in simulating the packet loss probability, our multifractal tra$c model provides a better "t than that obtained by using a fractional Brownian motion model. Copyright 2001 John Wiley & Sons, Ltd.