Bayesian inference for double Pareto lognormal queues

TL;DR

This paper develops a Bayesian estimation method for the double Pareto lognormal distribution, enabling analysis of complex queueing systems with heavy-tailed data, especially in internet traffic and risk management.

Contribution

It introduces a Bayesian approach for the dPlN distribution and applies it to analyze queueing systems lacking closed-form Laplace transforms.

Findings

Effective Bayesian estimation for dPlN distribution.

Application to analyze heavy-tailed queueing systems.

Approximate Laplace transforms facilitate analysis.

Abstract

In this article we describe a method for carrying out Bayesian estimation for the double Pareto lognormal (dPlN) distribution which has been proposed as a model for heavy-tailed phenomena. We apply our approach to estimate the $\mathit{dPlN}/M/1$ and $M/\mathit{dPlN}/1$ queueing systems. These systems cannot be analyzed using standard techniques due to the fact that the dPlN distribution does not possess a Laplace transform in closed form. This difficulty is overcome using some recent approximations for the Laplace transform of the interarrival distribution for the $\mathit{Pareto}/M/1$ system. Our procedure is illustrated with applications in internet traffic analysis and risk theory.