A Particular Collection of Service Time Distributions Parameters Study and Impact in some MGinf System Busy Period and Busy Cycle Parameters

TL;DR

This paper investigates how specific service time distribution parameters affect the analysis of MGinf queue systems, focusing on busy period and cycle characteristics, and proposes methods to address associated challenges.

Contribution

It introduces a study of particular service time distribution parameters and their impact on MGinf system busy periods and cycles, providing computational approaches for these metrics.

Findings

Computed busy cycle renewal function for MGinf systems

Analyzed peakedness and modified peakedness in busy periods

Identified challenges with moments of service time distributions

Abstract

The problems arising when the moments of service time distributions, for which the MGinf queue system busy period and busy cycle become very easy to study, are presented and it is shown how to overcome them. The busy cycle renewal function and the peakedness and the modified peakedness for the MGinf busy period and busy cycle in the case of those service time distributions are also computed.