Laplace Transform Effectiveness in the MGinf Queue Busy Period Probabilistic Study

TL;DR

This paper explores the use of Laplace transforms to analyze the busy period distribution in MGinf queues and develops an algorithm for global service time distribution in queue networks.

Contribution

It introduces a novel application of Laplace transforms to the MGinf queue busy period and proposes an algorithm for global service time distribution in queue networks.

Findings

Derived the tail Laplace transform for MGinf queue busy period

Developed an algorithm for global service time distribution in queue networks

Enhanced understanding of queue busy period analysis

Abstract

The Laplace transform is a widely used tool in the study of probability distributions, often allowing for a probability density functions and distribution functions simpler determination and being a moments generating function. In this paper it is considered a situation not so simple, as it is the case of the MGinf queue busy period length distribution. Attention will also be given the respective tail Laplace transform. Then, in the context of an open queues network, which nodes behave as MGinf queues, the Laplace transform will be used to construct an algorithm to determine the Laplace transform of the global service time length of a customer during their stay on the network distribution.