URN Modeling for Heavy-Tailed Phenomena
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Abstract
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.