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.

Keywords:

• Excess function
• Heavy tails
• Traffic modeling

Mathematics Subject Classification:

• Primary 62N09
• Secondary 60K250

View correction statement:

Corrections to: A Discrete-Time Approach for Heavy-Tailed Modeling

Notes

¹A random variable X is said to be heavy-tailed if its survival function decays according to P(X > x)∼ x ^−α for large values of x, and for α > 0.