URN Modeling for Heavy-Tailed Phenomena

During the last decade, it was clear that the use of Poisson processes for modeling network traffic underestimated certain important performance measures such as blocking or queueing delay, among others. Researches around the world agree with the presence of heavy-tail behavior in almost all the data traffic’s metrics, such as connection arrivals, file sizes, central processing unit (CPU) time demands of UNIX processes, etc. As a result, during the next few years, heavy-tailed distributions will play a principal role in the modelling and developing of telecommunications systems. Due to the nature of data traffic, researches demand a discrete heavy-tail distribution, perfectly well described, that enables them to reflect the impact of the two states present in all digital systems (on/off, successful/failed, connect/disconnected, enabled/disabled) in the tail decay. At the present time, there is no distribution with this high degree of flexibility. This thesis completes the description of the discrete heavy-tail distribution introduced in [24] by getting their moments and variance derived from a rigorous generating functions analysis. It validates the model’s heavy-tail nature through mean excess functions and some related plots such as the Quantile-Quantile or Probability-Probability plot. Also, the model’s stability and their match with the Pareto distribution are investigated. This work concludes with a discussion about the initial conditions influence in the model’s tail decay.