Stochastic Processes in Networks of Queues with Exponential Service Times and only one Class of Customers

TL;DR

This paper analyzes stochastic processes in queue networks with exponential service times and a single customer class, focusing on Jackson and Gordon-Newell models, providing detailed insights into their behavior.

Contribution

It offers a detailed study of Jackson and Gordon-Newell queue networks with exponential service times, highlighting their stochastic process properties and specific challenges.

Findings

Detailed characterization of queue network stochastic processes

Insights into the behavior of single-class customer models

Analysis of open and closed queue network models

Abstract

Two networks of queues models, presented initially by Jackson, in the open case, and Gordon and Newell, in the closed case, stochastic processes are presented and studied in some of their details and problems. The service times are exponentially distributed and there is only one class of customers.