A Discrete-Time Approach for Heavy-Tailed Modeling

Abstract

It is important in teletraffic modeling to provide mathematical models to study and evaluate performance. We introduce a traffic source based on Polya's urn model and study this in a semi-Markov process and relate the heavy-tailed characteristics and long-range dependence to the model parameters. The first and second moments are obtained from excess measures. Tail decay and long-range dependence are shown to be adequately engineered by selection of the parameters. Q–Q plots show agreement of the proposed model to Paretian-type distributions. The model could be used in applications such as queueing theory, networking, etc.