A Specific $M|G|\infty$ Queue System Busy Period and Busy Cycle Distributions and Parameters

TL;DR

This paper analyzes the transient behavior of the M|G|∞ queue system by solving a Riccati equation, identifying service time distributions, and studying the probabilistic properties of busy periods and cycles.

Contribution

It introduces a specific collection of service time distributions for the M|G|∞ queue and derives their properties, advancing understanding of the system's transient dynamics.

Findings

Derived a Riccati equation for the queue's transient analysis

Identified a collection of service time distributions relevant to the system

Analyzed the probabilistic properties of busy periods and cycles

Abstract

Solving a Riccati equation, induced by the study of the transient behaviour of the MGInf queue system, a collection of service times distributions is determined. For the MGInf queue, which service time distribution is a member of that collection, the busy period and busy cycle probabilistic studies are performed. In extra, the properties of that distributions collection are deduced and presented.