The Age or Excess of the MGinf Queue Busy Cycle Mean Value

TL;DR

This paper investigates the age and excess of the busy cycle in MGinf queue systems, providing approximate and exact results, especially for exponential distributions, with bounds for complex cases, relevant to reliability and performance analysis.

Contribution

It offers new analytical results and bounds for the busy cycle performance measure in MGinf queues, focusing on exponential and related distributions.

Findings

Exact results for exponential distributions

Bounds for non-exponential service distributions

Analysis of the busy cycle's performance measure

Abstract

In this work, approximate and exact results concerning a performance measure of the MGinf system, the age or the excess of the busy cycle, are presented. It will be seen that it is also a measure of the busy period performance. Service distributions for which it is given for a simple expression and others for which this does not happen are considered. For this last case, bounds are deduced. A special emphasis is given to the exponential distribution and to those related with it, useful in reliability theory.