Introduction and Overview

Abstract

In this book, we discuss iterative methods and Markovian models for queuing and manufacturing systems. We are interested in obtaining the steady-state probability distributions of these systems because much important system performance information such as the blocking probability, throughput, and average running cost of the system can be written in terms of this probability distribution. In some simple situations, it is possible to derive the analytical or an approximated steady-state probability distribution for a queuing or manufacturing system. But very often solving the steady-state probability distribution is a difficult task. Iterative methods and simulation techniques are common and powerful tools for solving the captured problems. The main focus of this book is the application of iterative methods in solving Markovian queuing and limiting probability systems. For simulation methods, we refer interested readers to the textbooks of references [86, 93, 95].