Communication Networks Performance Analysis of Multifractal Network Traffic

In this paper we present some new results in the framework of multifractal performance analysis including both the characterization and modeling of multifractal network traffic, and also the multifractal queueing performance analysis. We first propose a new multifractal traffic model for network traffic based on the combination of a multiplicative cascade with an independent lognormal process. This traffic model is able to provide a very accurate fit to the multifractal characteristics of data traffic including both the scaling function and the moment factor, but it is also simple enough from a practical point of view having only three parameters. In addition, the model features many important properties observed in data traffic including LRD, multifractality and lognormality. We also present an approximation for the queue tail asymptotics in an infinite capacity single server queue serviced at a constant rate driven by a general multifractal input process. We show that in the special and important case of the monofractal fractional Brownian motion (fBm) input traffic our result gives the well-known Weibullian tail. We prove that the class of Gaussian processes with scaling properties is in the class of monofractal processes and we derive the related characterization functions. Applying the approximation we provide a new practical method for queueing performance estimation of general multifractal traffic. Finally, we present a practical case study to show the practical application of our framework for measured data traffic and also to validate both our multifractal model and our queueing results.