Computing Customers Sojourn Times in Jackson Networks Distribution Functions and Moments

TL;DR

This paper reviews statistical results on customer sojourn times in Jackson networks, focusing on numerical methods for computing their distribution functions and moments, which are crucial for performance analysis in service and technology systems.

Contribution

It compiles and presents known statistical results on sojourn time distributions in Jackson networks, emphasizing numerical computation techniques.

Findings

Provides methods to compute distribution functions of sojourn times.

Offers techniques to calculate moments of sojourn time distributions.

Highlights applications in healthcare and telecommunications networks.

Abstract

Jackson queuing networks have a lot of practical applications, mainly in services and technologic devices. For the first case, an example are the healthcare networks and, for the second, the computation and telecommunications networks. Evidently the time that a customer (a person, a job, a message) spends in this kind of systems, its sojourn time, is an important measure of its performance, among others. In this work, the practical statistical known results about the sojourn time of a customer, in a Jackson network, distribution are collected and presented. And an emphasis is set on the numerical methods applicable to compute the distribution function and the moments.