Queueing analysis is a vital tool used in the evaluation of system
performance. Applications of queueing analysis cover a wide
spectrum from bank automated teller machines to transportation and
communications data networks.

Fully revised, this second edition of a popular book contains
the significant addition of a new chapter on Flow & Congestion
Control and a section on Network Calculus among other new sections
that have been added to remaining chapters. An introductory text,
Queueing Modelling Fundamentals focuses on queueing
modelling techniques and applications of data networks, examining
the underlying principles of isolated queueing systems. This book
introduces the complex queueing theory in simple language/proofs to
enable the reader to quickly pick up an overview to queueing theory
without utilizing the diverse necessary mathematical tools. It
incorporates a rich set of worked examples on its applications to
communication networks.

Features include:

* Fully revised and updated edition with significant new chapter
on Flow and Congestion Control as-well-as a new section on Network
Calculus

* A comprehensive text which highlights both the theoretical
models and their applications through a rich set of worked
examples, examples of applications to data networks and performance
curves

* Provides an insight into the underlying queuing principles and
features step-by-step derivation of queueing results

* Written by experienced Professors in the field

Queueing Modelling Fundamentals is an introductory text
for undergraduate or entry-level post-graduate students who are
taking courses on network performance analysis as well as those
practicing network administrators who want to understand the
essentials of network operations. The detailed step-by-step
derivation of queueing results also makes it an excellent text for
professional engineers.

Chee-Hock Ng, Nanyang Technological University, Singapore
Chee-Hock Ng is currently an Associate Professor in the School of Electrical & Electronic Engineering, Nanyang Technological University (NTU). He is also serving as an external examiner and assessor to the SIM University for its computer science programmes. The author of the first edition of "Queueing Modelling Fundamentals", Chee-Hock Ng runs short courses to the industry and other statuary bodies in the area of networking.? A Chartered Engineer and a Senior Member of IEEE, he has also published many papers in international journals and conferences in the areas of networking.

Boon-Hee Soong, Nanyang Technological University, Singapore
Soong Boon-Hee is currently an Associate Professor with the School of Electrical and Electronic Engineering, Nanyang Technological University. Previously a Visiting Research Fellow at the Department of Electrical and Electronic Engineering, Imperial College, London, under the Commonwealth Fellowship Award, he has served as a consultant for many companies including Mobile IP in a recent technical field trial of Next-Generation Wireless LAN initiated by IDA (InfoComm Development Authority, Singapore). Boon-Hee Soong was awarded the Tan Chin Tuan Fellowship in 2004. Author of over 100 international journals, book chapters and conference papers, he is currently a Senior member of IEEE and a member of ACM.

Fully revised, this second edition of a popular book contains the significant addition of a new chapter on Flow & Congestion Control and a section on Network Calculus among other new sections that have been added to remaining chapters. An introductory text, Queueing Modelling Fundamentals focuses on queueing modelling techniques and applications of data networks, examining the underlying principles of isolated queueing systems. This book introduces the complex queueing theory in simple language/proofs to enable the reader to quickly pick up an overview to queueing theory without utilizing the diverse necessary mathematical tools. It incorporates a rich set of worked examples on its applications to communication networks.

Features include:

• Fully revised and updated edition with significant new chapter on Flow and Congestion Control as-well-as a new section on Network Calculus
• A comprehensive text which highlights both the theoretical models and their applications through a rich set of worked examples, examples of applications to data networks and performance curves
• Provides an insight into the underlying queuing principles and features step-by-step derivation of queueing results
• Written by experienced Professors in the field

Queueing Modelling Fundamentals is an introductory text for undergraduate or entry-level post-graduate students who are taking courses on network performance analysis as well as those practicing network administrators who want to understand the essentials of network operations. The detailed step-by-step derivation of queueing results also makes it an excellent text for professional engineers.

List of Tables xi

List of Illustrations xiii

Preface xvii

1. Preliminaries 1

1.1 Probability Theory 1

1.1.1 Sample Spaces and Axioms of Probability 2

1.1.2 Conditional Probability and Independence 5

1.1.3 Random Variables and Distributions 7

1.1.4 Expected Values and Variances 12

1.1.5 Joint Random Variables and Their Distributions 16

1.1.6 Independence of Random Variables 21

1.2 z-Transforms - Generating Functions 22

1.2.1 Properties of z-Transforms 23

1.3 Laplace Transforms 28

1.3.1 Properties of the Laplace Transform 29

1.4 Matrix Operations 32

1.4.1 Matrix Basics 32

1.4.2 Eigenvalues, Eigenvectors and Spectral Representation 34

1.4.3 Matrix Calculus 36

Problems 39

2. Introduction to Queueing Systems 43

2.1 Nomenclature of a Queueing System 44

2.1.1 Characteristics of the Input Process 45

2.1.2 Characteristics of the System Structure 46

2.1.3 Characteristics of the Output Process 47

2.2 Random Variables and their Relationships 48

2.3 Kendall Notation 50

2.4 Little's Theorem 52

2.4.1 General Applications of Little's Theorem 54

2.4.2 Ergodicity 55

2.5 Resource Utilization and Traffic Intensity 56

2.6 Flow Conservation Law 57

2.7 Poisson Process 59

2.7.1 The Poisson Process - A Limiting Case 59

2.7.2 The Poisson Process - An Arrival Perspective 60

2.8 Properties of the Poisson Process 62

2.8.1 Superposition Property 62

2.8.2 Decomposition Property 63

2.8.3 Exponentially Distributed Inter-arrival Times 64

2.8.4 Memoryless (Markovian) Property of Inter-arrival Times 64

2.8.5 Poisson Arrivals During a Random Time Interval 66

Problems 69

3. Discrete and Continuous Markov Processes 71

3.1 Stochastic Processes 72

3.2 Discrete-time Markov Chains 74

3.2.1 Definitions of Discrete-time Markov Chains 75

3.2.2 Matrix Formulation of State Probabilities 79

3.2.3 General Transient Solutions for State Probabilities 81

3.2.4 Steady-state Behaviour of a Markov Chain 86

3.2.5 Reducibility and Periodicity of a Markov Chain 88

3.2.6 Sojourn Times of a Discrete-time Markov Chain 90

3.3 Continuous-time Markov Chains 91

3.3.1 Definition of Continuous-time Markov Chains 9…