Networks of Queues Models with Several Classes of Customers and Exponential Service Times

TL;DR

This paper introduces a Markov chain model for open and closed queueing networks with multiple customer classes and exponential service times, providing a method to determine key network characteristics without explicit stationary probabilities.

Contribution

It presents a novel Markov chain approach that simplifies analysis of complex queueing networks with multiple classes and exponential services, overcoming previous computational challenges.

Findings

Provides a Markov chain model for open networks with multiple classes

Simplifies analysis of closed networks under similar conditions

Enables determination of network characteristics without explicit stationary probabilities

Abstract

The main target of this paper is to present the Markov chain C that, not giving explicitly the queue lengths stationary probabilities, has the necessary information to its determination for open networks of queues with several classes of customers and exponential service times, allowing to overcome ingeniously this problem. The situation for closed networks, in the same conditions, much easier is also presented.