Queueing modelling fundamentals : with applications in communication networks

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.

Author Notes

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.

List of Tables	p. xi
List of Illustrations	p. xiii
Preface	p. xvii
1 Preliminaries	p. 1
1.1 Probability Theory	p. 1
1.1.1 Sample Spaces and Axioms of Probability	p. 2
1.1.2 Conditional Probability and Independence	p. 5
1.1.3 Random Variables and Distributions	p. 7
1.1.4 Expected Values and Variances	p. 12
1.1.5 Joint Random Variables and Their Distributions	p. 16
1.1.6 Independence of Random Variables	p. 21
1.2 z-Transforms - Generating Functions	p. 22
1.2.1 Properties of z-Transforms	p. 23
1.3 Laplace Transforms	p. 28
1.3.1 Properties of the Laplace Transform	p. 29
1.4 Matrix Operations	p. 32
1.4.1 Matrix Basics	p. 32
1.4.2 Eigenvalues, Eigenvectors and Spectral Representation	p. 34
1.4.3 Matrix Calculus	p. 36
Problems	p. 39
2 Introduction to Queueing Systems	p. 43
2.1 Nomenclature of a Queueing System	p. 44
2.1.1 Characteristics of the Input Process	p. 45
2.1.2 Characteristics of the System Structure	p. 46
2.1.3 Characteristics of the Output Process	p. 47
2.2 Random Variables and their Relationships	p. 48
2.3 Kendall Notation	p. 50
2.4 Little's Theorem	p. 52
2.4.1 General Applications of Little's Theorem	p. 54
2.4.2 Ergodicity	p. 55
2.5 Resource Utilization and Traffic Intensity	p. 56
2.6 Flow Conservation Law	p. 57
2.7 Poisson Process	p. 59
2.7.1 The Poisson Process - A Limiting Case	p. 59
2.7.2 The Poisson Process - An Arrival Perspective	p. 60
2.8 Properties of the Poisson Process	p. 62
2.8.1 Superposition Property	p. 62
2.8.2 Decomposition Property	p. 63
2.8.3 Exponentially Distributed Inter-arrival Times	p. 64
2.8.4 Memoryless (Markovian) Property of Inter-arrival Times	p. 64
2.8.5 Poisson Arrivals During a Random Time Interval	p. 66
Problems	p. 69
3 Discrete and Continuous Markov Processes	p. 71
3.1 Stochastic Processes	p. 72
3.2 Discrete-time Markov Chains	p. 74
3.2.1 Definitions of Discrete-time Markov Chains	p. 75
3.2.2 Matrix Formulation of State Probabilities	p. 79
3.2.3 General Transient Solutions for State Probabilities	p. 81
3.2.4 Steady-state Behaviour of a Markov Chain	p. 86
3.2.5 Reducibility and Periodicity of a Markov Chain	p. 88
3.2.6 Sojourn Times of a Discrete-time Markov Chain	p. 90
3.3 Continuous-time Markov Chains	p. 91
3.3.1 Definition of Continuous-time Markov Chains	p. 91
3.3.2 Sojourn Times of a Continuous-time Markov Chain	p. 92
3.3.3 State Probability Distribution	p. 93
3.3.4 Comparison of Transition-rate and Transition-probability Matrices	p. 95
3.4 Birth-Death Processes	p. 96
Problems	p. 100
4 Single-Queue Markovian Systems	p. 103
4.1 Classical M/M/1 Queue	p. 104
4.1.1 Global and Local Balance Concepts	p. 106
4.1.2 Performance Measures of the M/M/1 System	p. 107
4.2 PASTA - Poisson Arrivals See Time Averages	p. 110
4.3 M/M/1 System Time (Delay) Distribution	p. 111
4.4 M/M/1/S Queueing Systems	p. 118
4.4.1 Blocking Probability	p. 119
4.4.2 Performance Measures of M/M/1/S Systems	p. 120
4.5 Multi-server Systems - M/M/m	p. 124
4.5.1 Performance Measures of M/M/m Systems	p. 126
4.5.2 Waiting Time Distribution of M/M/m	p. 127
4.6 Erlang's Loss Queueing Systems - M/M/m/m Systems	p. 129
4.6.1 Performance Measures of the M/M/m/m	p. 130
4.7 Engset's Loss Systems	p. 131
4.7.1 Performance Measures of M/M/m/m with Finite Customer Population	p. 133
4.8 Considerations for Applications of Queueing Models	p. 134
Problems	p. 139
5 Semi-Markovian Queueing Systems	p. 141
5.1 The M/G/1 Queueing System	p. 142
5.1.1 The Imbedded Markov-chain Approach	p. 142
5.1.2 Analysis of M/G/1 Queue Using Imbedded Markov-chain Approach	p. 143
5.1.3 Distribution of System State	p. 146
5.1.4 Distribution of System Time	p. 147
5.2 The Residual Service Time Approach	p. 148
5.2.1 Performance Measures of M/G/1	p. 150
5.3 M/G/1 with Service Vocations	p. 155
5.3.1 Performance Measures of M/G/1 with Service Vacations	p. 156
5.4 Priority Queueing Systems	p. 158
5.4.1 M/G/1 Non-preemptive Priority Queueing	p. 158
5.4.2 Performance Measures of Non-preemptive Priority	p. 160
5.4.3 M/G/1 Pre-emptive Resume Priority Queueing	p. 163
5.5 The G/M/1 Queueing System	p. 165
5.5.1 Performance Measures of GI/M/1	p. 166
Problems	p. 167
6 Open Queueing Networks	p. 169
6.1 Markovian Queries in Tandem	p. 171
6.1.1 Analysis of Tandem Queues	p. 175
6.1.2 Burke's Theorem	p. 176
6.2 Applications of Tandem Queues in Data Networks	p. 178
6.3 Jackson Queueing Networks	p. 181
6.3.1 Performance Measures for Open Networks	p. 186
6.3.2 Balance Equations	p. 190
Problems	p. 193
7 Closed Queueing Networks	p. 197
7.1 Jackson Closed Queueing Networks	p. 197
7.2 Steady-state Probability Distribution	p. 199
7.3 Convolution Algorithm	p. 203
7.4 Performance Measures	p. 207
7.5 Mean Value Analysis	p. 210
7.6 Application of Closed Queueing Networks	p. 213
Problems	p. 214
8 Markov-Modulated Arrival Process	p. 217
8.1 Markov-modulated Poisson Process (MMPP)	p. 218
8.1.1 Definition and Model	p. 218
8.1.2 Superposition of MMPPs	p. 223
8.1.3 MMPP/G/1	p. 225
8.1.4 Applications of MMPP	p. 226
8.2 Markov-modulated Bernoulli Process	p. 227
8.2.1 Source Model and Definition	p. 227
8.2.2 Superposition of N Identical MMBPs	p. 228
8.2.3 [Sigma]MMBP/D/1	p. 229
8.2.4 Queue Length Solution	p. 231
8.2.5 Initial Conditions	p. 233
8.3 Markov-modulated Fluid Flow	p. 233
8.3.1 Model and Queue Length Analysis	p. 233
8.3.2 Applications of Fluid Flow Model to ATM	p. 236
8.4 Network Calculus	p. 236
8.4.1 System Description	p. 237
8.4.2 Input Traffic Characterization - Arrival Curve	p. 239
8.4.3 System Characterization - Service Curve	p. 240
8.4.4 Min-Plus Algebra	p. 241
9 Flow and Congestion Control	p. 243
9.1 Introduction	p. 243
9.2 Quality of Service	p. 245
9.3 Analysis of Sliding Window Flow Control Mechanisms	p. 246
9.3.1 A Simple Virtual Circuit Model	p. 246
9.3.2 Sliding Window Model	p. 247
9.4 Rate Based Adaptive Congestion Control	p. 257
References	p. 259
Index	p. 265

Available:*

On Order

Summary

Summary

Author Notes

Table of Contents