Modelling and control of broadband traffic using multiplicative multifractal cascades

Abstract. We present the results on the modelling and synthesis of broadband traffic processes namely ethernet inter-arrival times using the VVGM (variable variance gaussian multiplier) multiplicative multifractal model. This model is shown to be more appropriate for modelling network traffic which possess time varying scaling/self-similarity and burstiness. The model gives a simple and efficient technique to synthesise Ethernet inter-arrival times. The results of the detailed statistical and multifractal analysis performed on the original and the synthesised traces are presented and the performance is compared with other models in the literature, such as the Poisson process, and the Multifractal Wavelet Model (MWM) process. It is also shown empirically that a single server queue preserves the multifractal character of the process by analysing its inter-departure process when fed with the multifractal traces. The result of the existence of a global-scaling exponent for multifractal cascades and its application in queueing theory are discussed. We propose tracking and control algorithms for controlling network congestion with bursty traffic modelled by multifractal cascade processes, characterised by the Holder exponents, the value of which at an interval indicates the burstiness in the traffic at that point. This value has to be estimated and used for the estimation of the congestion and predictive control of the traffic in broadband networks. The estimation can be done by employing wavelet transforms and a Kalman filter based predictor for predicting the burstiness of the traffic.