Modeling and analysis of telecommunications networks / Jeremiah F. Hayes, Thimma V.J. Ganesh Babu.

Format:

Book

Author/Creator:

Hayes, Jeremiah F., 1934-

Contributor:

Babu, Thimma V.J. Ganesh.

Alumni and Friends Memorial Book Fund.

Language:

English

Subjects (All):

Telecommunication systems.

Physical Description:

xx, 393 pages : illustrations ; 25 cm

Place of Publication:

Hoboken, N.J. : Wiley-Interscience, [2004]

Summary:

This book covers at an advanced level mathematical methods for analysis of telecommunication networks. The book concentrates on various call models used in telecommunications such as quality of service (QoS) in packet-switched Internet Protocol (IP) networks, Asynchronous Transfer Mode (ATM), and Time Division Multiplexing (TDM). Professionals, researchers, and graduate and advanced undergraduate students of telecommunications will benefit from this invaluable guidebook. An Instructor's Manual presenting detailed solutions to all the problems in the book is available online from the Wiley editorial department. An Instructor Support FTP site is also available.

Contents:

Retrieving Files from the Wiley FTP and Internet Sites xix

1 Performance Evaluation in Telecommunications 1

1.1 Introduction: The Telephone Network 1

1.1.1 Customer Premises Equipment 1

1.1.2 The Local Network 2

1.1.3 Long-Haul Network 4

1.1.4 Switching 4

1.1.5 The Functional Organization of Network Protocols 6

1.2 Approaches to Performance Evaluation 8

1.3 Queueing Models 9

1.3.1 Basic Form 9

1.3.2 A Brief Historical Sketch 10

1.4 Computational Tools 13

2 Probability and Random Processes Review 17

2.1 Basic Relations 17

2.1.1 Set Functions and the Axioms of Probability 17

2.1.2 Conditional Probability and Independence 20

2.1.3 The Law of Total Probability and Bayes' Rule 21

2.2 Random Variables

Probability Distributions and Densities 22

2.2.1 The Cumulative Distribution Function 22

2.2.2 Discrete Random Variables 23

2.2.3 Continuous Random Variables 31

2.3 Joint Distributions of Random Variables 38

2.3.1 Probability Distributions 38

2.3.2 Joint Moments 40

2.3.3 Autocorrelation and Autocovariance Functions 41

2.4 Linear Transformations 42

2.4.1 Single Variable 42

2.4.2 Sums of Random Variables 42

2.5 Transformed Distributions 46

2.6 Inequalities and Bounds 47

2.7 Markov Chains 52

2.7.1 The Memoryless Property 52

2.7.2 State Transition Matrix 53

2.7.3 Steady-State Distribution 56

2.8 Random Processes 61

2.8.1 Defintion: Ensemble of Functions 61

2.8.2 Stationarity and Ergodicity 61

2.8.3 Markov Processes 63

3 Application of Birth and Death Processes to Queueing Theory 67

3.1 Elements of the Queueing Model 67

3.2 Little's Formula 69

3.2.1 A Heuristic 69

3.2.2 Graphical Proof 70

3.2.3 Basic Relationship for the Single-Server Queue 73

3.3 The Poisson Process 74

3.3.1 Basic Properties 74

3.3.2 Alternative Characterizations of the Poisson Process 75

3.3.3 Adding and Splitting Poisson Processes 78

3.3.4 Pure Birth Processes 79

3.3.5 Poisson Arrivals See Time Averages (PASTA) 81

3.4 Birth and Death Processes: Application to Queueing 82

3.4.1 Steady-State Solution 82

3.4.2 Queueing Models 85

3.4.3 The M/M/1 Queue

Infinite Waiting Room 86

3.4.4 The M/M/1/L Queue

Finite Waiting Room 89

3.4.5 The M/M/S Queue

Infinite Waiting Room 91

3.4.6 The M/M/S/L Queue

Finite Waiting Room 95

3.4.7 Finite Sources 97

3.5 Method of Stages 98

3.5.1 Laplace Transform and Averages 98

3.5.2 Insensitivity Property of Erlang B 100

3.5.3 The Erlang B Blocking Formula: N Lines, Homogeneous Traffic 103

4 Networks of Queues: Product Form Solution 113

4.1 Introduction: Jackson Networks 113

4.2 Reversibility: Burke's Theorem 114

4.2.1 Reversibility Defined 114

4.2.2 Reversibility and Birth and Death Processes 116

4.2.3 Departure Process from the M/M/S Queue: Burke's Theorem 118

4.3 Feedforward Networks 119

4.3.1 A Two-Node Example 119

4.3.2 Feedforward Networks: Application of Burke's Theorem 120

4.3.3 The Traffic Equation 121

4.4 Product Form Solution for Open Networks 123

4.4.1 Flows Within Feedback Paths 123

4.4.2 Detailed Derivation for a Two-Node Network 124

4.4.3 N-Node Open Jackson Networks 127

4.4.4 Average Message Delay in Open Networks 132

4.4.5 Store-and-Forward Message-Switched Networks 134

4.4.6 Capacity Allocation 138

4.5 Closed Jackson Networks 139

4.5.1 Traffic Equation 139

4.5.2 Global Balance Equation

Solution 141

4.5.3 Normalization Constant

Convolution Algorithm 142

4.5.4 Extension to the Infinite Server Case 146

4.5.5 Mean Value Analysis of Closed Chains 147

4.5.6 Application to General Networks 149

4.6 BCMP Networks 150

4.6.1 Overview of BCMP Networks 150

4.6.2 Single Node

Exponential Server 151

4.6.3 Single Node

Infinite Server 152

4.6.4 Single Node

Processor Sharing 156

4.6.5 Single Node

Last Come First Served (LCFS) 158

4.7 Networks of BCMP Queues 161

4.7.1 Store-and-Forward Message-Switched Nodes 163

4.7.2 Example: Window Flow Control

A Closed Network Model 170

4.7.3 Cellular Radio 175

5 Markov Chains: Application to Multiplexing and Access 187

5.1 Time-Division Multiplexing 187

5.2 The Arrival Process 188

5.2.1 Packetization 188

5.2.2 Compound Arrivals 189

5.3 Asynchronous Time-Division Multiplexing 190

5.3.1 Finite Buffer 192

5.3.2 Infinite Buffer 195

5.4 Synchronous Time-Division Multiplexing 197

5.4.1 Application of Rouche's Theorem 199

5.4.2 Calculations Involving Rouche's Theorem 201

5.4.3 Message Delay 203

5.5 Random Access Techniques 207

5.5.1 Introduction to ALOHA 207

5.5.2 Analysis of Delay 210

6 The M/G/1 Queue: Imbedded Markov Chains 219

6.1 The M/G/1 Queue 219

6.1.1 Imbedded Markov Chains 220

6.1.2 Distribution of Message Delay: FCFS 222

6.1.3 Residual Life Distribution: Alternate Derivation of the Pollaczek-Khinchin Formula 231

6.1.4 Variation for the Initiator of a Busy Period 234

6.1.5 Busy Period of the M/G/1 Queue 237

6.2 The G/M/1 Queue 241

6.3 Priority Queues 244

6.3.1 Preemptive Resume Discipline 245

6.3.2 L-Priority Classes 252

6.3.3 Nonpreemptive Priorities 256

6.4 Polling 265

6.4.1 Basic Model: Applications 265

6.4.2 Average Cycle Time 267

6.4.3 Average Delay: Exhaustive, Gated, and Limited Service 267

7 Fluid Flow Analysis 281

7.1 On-Off Sources 281

7.1.1 Single Source 281

7.1.2 Multiple Sources 284

7.2 Infinite Buffers 286

7.2.1 The Differential Equation for Buffer Occupancy 286

7.2.2 Derivation of Eigenvalues 289

7.2.3 Derivation of the Eigenvectors 292

7.2.4 Derivation of Coefficients 295

7.3 Finite Buffers 298

7.4 More General Sources 300

7.5 Analysis: Leaky Bucket 300

7.6 Equivalent Bandwidth 303

7.7 Long-Range-Dependent Traffic 304

7.7.2 A Matching Technique for LRD Traffic Using the Fluid Flow Model 306

8 The Matrix Geometric Techniques 313

8.2 Arrival Processes 313

8.2.1 The Markov Modulated Poisson Process (MMPP) 314

8.2.2 The Batch Markov Arrival Process 316

8.2.3 Further Extensions 319

8.2.4 Solutions of Forward Equation for the Arrival Process 319

8.3 Imbedded Markov Chain Analysis 321

8.3.1 Revisiting the M/G/1 Queue 321

8.3.2 The Multidimensional Case 323

8.3.3 Application of Renewal Theory 328

8.3.4 Moments at Message Departure 334

8.3.5 Steady-State Queue Length at Arbitrary Points in Time 335

8.3.6 Moments of the Queue Length at Arbitrary Points in Time 336

8.3.7 Virtual Waiting Time 336

8.4 A Matching Technique for LRD Traffic 337

8.4.1 d MMPPs and Equivalents 337

8.4.2 A Fitting Algorithm 339

Appendix 8A Derivation of Several Basic Equations Used in Text 343

Appendix 8B Derivation of Variance and Covariance Functions of Two-State MMPP 347

9 Monte Carlo Simulation 359

9.1 Simulation and Statistics 359

9.1.2 Sample Mean and Sample Variance 359

9.1.3 Confidence Intervals 361

9.1.4 Sample Sizes and Run Times 362

9.1.5 Histograms 364

9.1.6 Hypothesis Testing and the Chi-Square Test 368

9.2 Random-Number Generation 370

9.2.1 Pseudorandom Numbers 370

9.2.2 Generation of Continuous Random Variables 371

9.2.3 Discrete Random Variables

General Case 375

9.2.4 Generating Specific Discrete Random Variables 377

9.2.5 The Chi-Square Test Revisited 379

9.3 Discrete-Event Simulation 380

9.3.1 Time-Driven Simulation 380

9.3.2 Event-Driven Simulation 381

9.4 Variance Reduction Techniques 382

9.4.1 Common Random-Number Technique 383

9.4.2 Antithetic Variates 384

9.4.3 Control Variates 385

9.4.4 Importance Sampling 386.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Alumni and Friends Memorial Book Fund.

ISBN:

0471348457

OCLC:

53145676

Online:

Publisher description