Self-similar Sources Research Articles

Statistical modeling and design of discrete-time chaotic processes: advanced finite-dimensional tools and applications

With the aim of explaining the formal development behind the chaos-based modeling of network traffic and other similar phenomena, we generalize the tools presented in the paper of Setti et al. (see ibid., vol.90, p.662-90, May 2002) to the case of piecewise-affine Markov maps with a possibly infinite, but countable number of Markov intervals. Since, in doing so, we keep the dimensionality of the space of the observables finite, we still obtain a finite tensor-based framework. Nevertheless, the increased complexity of the model forces the use of tensors of functions whose handling is greatly simplified by extensive z transformation. With this, a systematic procedure is devised to write analytical expressions for the tensors that take into account the joint probability assignments needed to compute any-order expectations. As an example of use, this machinery is finally applied to the study of self-similarity of quantized processes both in the analysis of higher order phenomena as well as in the analysis and design of second-order self-similar sources suitable for artificial network traffic generation.

Modelling the self-similar behaviour of network traffic

Traditional Poisson or Markovian traffic models have been proven, by several studies, inappropriate for predicting the performance of networks with long-range dependent traffic. Thus, the use of conventional call admission control algorithms based on short-range dependent models cannot achieve the quality of service required by self-similar sources, since network performance is actually worse in terms of buffer overflow probability and delay. The variety of traffic types that depict long-range dependence creates the need for new models suitable for network design and congestion control mechanisms. In this paper, we present a call admission control (CAC) scheme for traffic with self-similar behaviour based on the notion of effective bandwidth. Our solution satisfies the quality of service requirements of the source, expressed in terms of buffer overflow probability, while taking into account the long-range dependence property of the traffic through the Hurst parameter. We base our CAC mechanism on a Gaussian model initially studied by Norros. We show that this model performs well in the case of one source as well as in the case of many aggregated sources. Our scheme assumes homogenous sources, each one represented by a fractional Gaussian noise process characterised by the mean bit rate and the self-similarity parameters (H, α). We study the estimation of ( H, α) from the real traffic and show the connection between their estimates. Finally, we present a way to calculate the equivalent capacity, which is necessary so that the aggregated stream will achieve the desired loss rate. In our simulation experiments, we used data collected from an IP over ATM high-speed link, connecting the National Research Network of Greece (GRnet) to the Trans-European network backbone (TEN-34), a part of the global Internet.

On the equivalent bandwidth of self-similar sources

This article presents a method for the computation of the equivalent bandwidth of an aggregate of heterogeneous self-similar sources, as well as the time scales of interest for queueing systems fed by a fractal Brownian motion (fBm) process. Moreover, the fractal leaky bucket, a novel policing mechanism capable of accurately monitoring self-similar sources, is introduced.