The pseudo-self-similar traffic model: application and validation

Since the early 1990¿s, a variety of studies has shown that network traffic, both for local- and wide-area networks, has self-similar properties. This led to new approaches in network traffic modelling because most traditional traffic approaches result in the underestimation of performance measures of interest. Instead of developing completely new traffic models, a number of researchers have proposed to adapt traditional traffic modelling approaches to incorporate aspects of self-similarity. The motivation for doing so is the hope to be able to reuse techniques and tools that have been developed in the past and with which experience has been gained. One such approach for a traffic model that incorporates aspects of self-similarity is the so-called pseudo self-similar traffic model. This model is appealing, as it is easy to understand and easily embedded in Markovian performance evaluation studies. In applying this model in a number of cases, we have perceived various problems which we initially thought were particular to these specific cases. However, we recently have been able to show that these problems are fundamental to the pseudo self-similar traffic model. In this paper we review the pseudo self-similar traffic model and discuss its fundamental shortcomings. As far as we know, this is the first paper that discusses these shortcomings formally. We also report on ongoing work to overcome some of these problems

Fitting World-Wide Web Request Traces with the EM-Algorithm

In recent years, several studies have shown that network traffic exhibits the property of self-similarity. Traditional (Poissonian) modelling approaches have been shown not to be able to describe this property and generally lead to the underestimation of interesting performance measures. Crovella and Bestavros have shown that network traffic that is due to World Wide Web transfers shows characteristics of self-similarity and they argue that this can be explained by the heavy-tailedness of many of the involved distributions. Considering these facts, developing methods which are able to handle self-similarity and heavy-tailedness is of great importance for network capacity planing purposes. In this paper we discuss two methods to fit hyper-exponential distributions to data sets which exhibit heavy-tails. One method is taken from the literature and shown to fall short. The other, new method, is shown to perform well in a number of case studies

Fitting World-Wide Web Request Traces with the EM-Algorithm

In recent years, various researchers have shown that network traffic that is due to world-wide web transfers shows characteristics of self-similarity and it has been argued that this can be explained by the heavy-tailedness of many of the involved distributions. Considering these facts, developing methods that are able to handle self-similarity and heavy-tailedness is of great importance for network capacity planning purposes.\ud \ud However, heavy-tailed distributions cannot be used so easily for analytical or numerical evaluation studies. To overcome this problem, in this paper, we approximate the empirical distributions by analytically more tractable, that is, hyper-exponential distributions. For that purpose, we present a new fitting algorithm based on the expectation-maximisation and show it to perform well both for pure traffic statistics as well as in queuing studies. \u