Fractional stable noise processes and their application to traffic modeling and fast simulation of broadband telecommunications networks

A great amount of research has been focused during the last few years on obtaining realistic models for the traffic generated by the users of telecommunications networks. Self-similarity and long-range dependence have been proved to be important features of aggregated traffic, and several models of this type have been proposed. These models, however, are applicable only to relatively slowly-varying traffic, since they are unable to capture the high level of burstiness of some types of information flows.;The main purpose of this research is to prove that aggregate traffic traces that present very high burstiness can also be accurately modeled with long-range dependent processes by using infinite-variance distributions for the marginal probability density function. Namely, we propose the use of alpha-stable distributions.;In order to prove the appropriateness of the model that we are proposing, different types of self-similar traffic traces (LAN/WAN, WWW, VBR video) are analyzed by estimating their self-similarity coefficient H, as well as the parameters of their marginal distributions. When comparing the real traces with our artificial traces, the agreement is evaluated both qualitatively (visually) and quantitatively (by means of the sample PDF to compare their marginal distribution, and the periodogram to compare their dynamic behavior). By analyzing different types of traffic traces, the model is shown to be flexible enough to be applied to simulate a variety of communications scenarios. An analytical proof, from basic principles, of the appropriateness of the proposed model is also given, as well as the conditions under which the Gaussian assumption is applicable.;As additional tools for the application of this novel model to the solution of a variety of telecommunications problems, algorithms for prediction of traffic behavior, fast generation of artificial traces, and fast simulation of systems involving traffic compatible with our model are given. In order to find an efficient algorithm for the generation of artificial traces of FSN processes, we approximate our random process by an auto regressive (AR) model based on the minimum dispersion (MD) principle. In order to derive this algorithm, we describe the dependence structure and define a prediction algorithm for both Linear- and Log-Fractional Stable Noise processes. The way this algorithm works is by estimating the next sample using values from the past, and by adding a random (alpha-stable) increment to this estimated value. To compare the artificial traces generated by the fast and the direct algorithms, we use again their sample PDF and their periodogram.;The prediction algorithm used in the fast traffic-generation method is generalized to estimate now the value of the random process at an arbitrary distance into the future. Prediction can be applied to the solution of a variety of problems, such as dynamic bandwidth allocation, buffer and bandwidth optimization inside a switch, etc.;Finally, a fast simulation algorithm is proposed based on the Importance Sampling technique. Previous theoretical results do not allow for a direct application of this technique to alpha-stable stochastic processes; therefore, mathematical manipulation and approximations are needed in order to achieve our goal. The appropriateness of our proposed method is evaluated by comparing results obtained via our algorithm and those acquired using direct (long) simulations.