Difference and differential equations with applications in queueing theory

Appropriate for students and practitioners alike, this book uniquely combines rich and interrelated areas of differential equations, difference equations, and queueing models along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform. It provides single-server, multiple-server, parallel, and series queue models with discussions on splitting, delayed-service, and delayed feedback. In addition, each chapter concludes with exercises featuring answers to select problems.

This book features a collection of topics that are used in stochastic processes and, particularly, in queueing theory. Differential equations, difference equations, and Markovian queues (as they relate to systems of linear differential difference equations) are presented, and the relationship between the methods and applications are thoroughly addressed"

Dedication ix Preface xii ONE Probability and Statistics, Outlines 1 1.1 Basic Definitions and Concepts of Probability 1 1.2. Discrete Random Variable and Probability Distribution Functions 8 1.3. Moments of a Discrete Random Variable 18 1.4. Continuous Random variables 22 1.5. Moments of a Continuous Random Variable 28 1.6. Continuous Probability Distribution Functions 29 1.7. Random Vector 47 1.8. Continuous Random Vector 53 1.9. Functions of Random variables 54 1.10. Basic Elements of Statistics 59 1.11. Inferential Statistics 72 1.12. Hypothesis Testing 80 1.13. Reliability 82 Chapter One Exercises 87 TWO Transforms 96 2.1. Fourier Transform 96 2.2. Laplace Transform 100 2.3. Transform 111 2.4. Probability Generating Function 118 Chapter Two Exercises 124 THREE Differential Equations 129 3.1. Basics Concepts and Definitions 129 3.2. Existence and Uniqueness 138 3.3. Separable Equations 140 3.4. Linear Differential Equation 150 3.5. Exact Differential Equations 154 3.6. Solution