Pareto Distribution Delay System Queueing Analyses Simulation Model Peak Traffic Modelling
Institute of Information Theories and Applications FOI ITHEA
The finding that Pareto distributions are adequate to model Internet packet interarrival times has
motivated the proposal of methods to evaluate steady-state performance measures of Pareto/D/1/k queues.
Some limited analytical derivation for queue models has been proposed in the literature, but their solutions are
often of a great mathematical challenge. To overcome such limitations, simulation tools that can deal with general
queueing system must be developed. Despite certain limitations, simulation algorithms provide a mechanism to
obtain insight and good numerical approximation to parameters of queues. In this work, we give an overview of
some of these methods and compare them with our simulation approach, which are suited to solve queues with
Generalized-Pareto interarrival time distributions. The paper discusses the properties and use of the Pareto
distribution. We propose a real time trace simulation model for estimating the steady-state probability showing the
tail-raising effect, loss probability, delay of the Pareto/D/1/k queue and make a comparison with M/D/1/k. The
background on Internet traffic will help to do the evaluation correctly. This model can be used to study the long-
tailed queueing systems. We close the paper with some general comments and offer thoughts about future work.