Considerations on $M|G|\infty$ Queue Busy Period Variance

TL;DR

This paper investigates the variance of the busy period in the $M|G| ext{infinity}$ queue, providing bounds based on limited distribution parameters, and explores conditions for exponentiality related to the coefficient of variation.

Contribution

It offers new bounds for the busy period variance depending only on certain parameters, and examines the exponentiality condition through the coefficient of variation.

Findings

Bounds for busy period variance depending on limited parameters.

Conditions for exponentiality of the busy period based on coefficient of variation.

Application of results to reliability, technological, and financial contexts.

Abstract

Some important results on the variance of the $M|G|\infty$ queue busy period are presented. Often, this parameter depends on the whole structure of the service time distribution. So, the importance of the bounds presented, depending only on some parameters. Also, some bounds for service time distributions important in reliability theory, with technological and financial applications, are presented and a particular stochastic ordination is explored to explain those results. Finally, an interesting result about the exponentiality of the MGInf queue busy period, resulting from the coefficient of variation study is shown.