Infinite Servers Queue Systems Busy Period Time Length Distribution and Parameters Study through Computational Simulation

TL;DR

This paper presents a FORTRAN simulation program for infinite servers queue systems, focusing on busy period distributions and parameters, especially when theoretical results are unavailable or intractable, to aid understanding through computational experiments.

Contribution

It introduces a simulation approach to study busy period distributions in infinite servers queues where theoretical analysis is difficult or impossible.

Findings

Simulation results provide insights into busy period distributions.

The program helps estimate parameters where analytical solutions are lacking.

Simulation aids in conjecturing properties of queue systems.

Abstract

A FORTRAN program to simulate the operation of infinite servers queues is presented in this work. Poisson arrivals processes are considered but not only. For many parameters of interest in queuing systems study or application, either there are not theoretical results or, existing, they are mathematically intractable what makes their utility doubtful. In this case a possible issue is to use simulation methods in order to get more useful results. Indeed, using simulation, some experiences may be performed and the respective results used to conjecture about certain queue systems interesting quantities. In this paper this procedure is followed to learn something more about quantities of interest for those infinite servers queue systems, in particular about busy period parameters and probability distributions.