Modeling and analysis of telecommunications networks

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Title:

Personal Author:

Hayes, Jeremiah F.

Publication Information:

Hoboken, NJ : John Wiley & Sons, 2004

ISBN:

9780471348450

Subject Term:

Telecommunication systems

Added Author:

Babu, Thimma V. J. Ganesh

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Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
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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.

Author Notes

Jeremiah F. Hayes, PhD, is recently retired as Distinguished Emeritus Professor of Electrical and Computer Engineering at Concordia University
Ganesh Babu, PhD, is a telecommunications consultant and part-time professor of Electrical and Computer Engineering at Concordia University

Preface	p. xiii
Retrieving Files from the Wiley FTP and Internet Sites	p. xix
1 Performance Evaluation in Telecommunications	p. 1
1.1 Introduction: The Telephone Network	p. 1
1.1.1 Customer Premises Equipment	p. 1
1.1.2 The Local Network	p. 2
1.1.3 Long-Haul Network	p. 4
1.1.4 Switching	p. 4
1.1.5 The Functional Organization of Network Protocols	p. 6
1.2 Approaches to Performance Evaluation	p. 8
1.3 Queueing Models	p. 9
1.3.1 Basic Form	p. 9
1.3.2 A Brief Historical Sketch	p. 10
1.4 Computational Tools	p. 13
Further Reading	p. 14
2 Probability and Random Processes Review	p. 17
2.1 Basic Relations	p. 17
2.1.1 Set Functions and the Axioms of Probability	p. 17
2.1.2 Conditional Probability and Independence	p. 20
2.1.3 The Law of Total Probability and Bayes' Rule	p. 21
2.2 Random Variables--Probability Distributions and Densities	p. 22
2.2.1 The Cumulative Distribution Function	p. 22
2.2.2 Discrete Random Variables	p. 23
2.2.3 Continuous Random Variables	p. 31
2.3 Joint Distributions of Random Variables	p. 38
2.3.1 Probability Distributions	p. 38
2.3.2 Joint Moments	p. 40
2.3.3 Autocorrelation and Autocovariance Functions	p. 41
2.4 Linear Transformations	p. 42
2.4.1 Single Variable	p. 42
2.4.2 Sums of Random Variables	p. 42
2.5 Transformed Distributions	p. 46
2.6 Inequalities and Bounds	p. 47
2.7 Markov Chains	p. 52
2.7.1 The Memoryless Property	p. 52
2.7.2 State Transition Matrix	p. 53
2.7.3 Steady-State Distribution	p. 56
2.8 Random Processes	p. 61
2.8.1 Defintion: Ensemble of Functions	p. 61
2.8.2 Stationarity and Ergodicity	p. 61
2.8.3 Markov Processes	p. 63
References	p. 64
Exercises	p. 64
3 Application of Birth and Death Processes to Queueing Theory	p. 67
3.1 Elements of the Queueing Model	p. 67
3.2 Little's Formula	p. 69
3.2.1 A Heuristic	p. 69
3.2.2 Graphical Proof	p. 70
3.2.3 Basic Relationship for the Single-Server Queue	p. 73
3.3 The Poisson Process	p. 74
3.3.1 Basic Properties	p. 74
3.3.2 Alternative Characterizations of the Poisson Process	p. 75
3.3.3 Adding and Splitting Poisson Processes	p. 78
3.3.4 Pure Birth Processes	p. 79
3.3.5 Poisson Arrivals See Time Averages (PASTA)	p. 81
3.4 Birth and Death Processes: Application to Queueing	p. 82
3.4.1 Steady-State Solution	p. 82
3.4.2 Queueing Models	p. 85
3.4.3 The M/M/1 Queue--Infinite Waiting Room	p. 86
3.4.4 The M/M/1/L Queue--Finite Waiting Room	p. 89
3.4.5 The M/M/S Queue--Infinite Waiting Room	p. 91
3.4.6 The M/M/S/L Queue--Finite Waiting Room	p. 95
3.4.7 Finite Sources	p. 97
3.5 Method of Stages	p. 98
3.5.1 Laplace Transform and Averages	p. 98
3.5.2 Insensitivity Property of Erlang B	p. 100
3.5.3 The Erlang B Blocking Formula: N Lines, Homogeneous Traffic	p. 103
References	p. 106
Exercises	p. 106
4 Networks of Queues: Product Form Solution	p. 113
4.1 Introduction: Jackson Networks	p. 113
4.2 Reversibility: Burke's Theorem	p. 114
4.2.1 Reversibility Defined	p. 114
4.2.2 Reversibility and Birth and Death Processes	p. 116
4.2.3 Departure Process from the M/M/S Queue: Burke's Theorem	p. 118
4.3 Feedforward Networks	p. 119
4.3.1 A Two-Node Example	p. 119
4.3.2 Feedforward Networks: Application of Burke's Theorem	p. 120
4.3.3 The Traffic Equation	p. 121
4.4 Product Form Solution for Open Networks	p. 123
4.4.1 Flows Within Feedback Paths	p. 123
4.4.2 Detailed Derivation for a Two-Node Network	p. 124
4.4.3 N-Node Open Jackson Networks	p. 127
4.4.4 Average Message Delay in Open Networks	p. 132
4.4.5 Store-and-Forward Message-Switched Networks	p. 134
4.4.6 Capacity Allocation	p. 138
4.5 Closed Jackson Networks	p. 139
4.5.1 Traffic Equation	p. 139
4.5.2 Global Balance Equation--Solution	p. 141
4.5.3 Normalization Constant--Convolution Algorithm	p. 142
4.5.4 Extension to the Infinite Server Case	p. 146
4.5.5 Mean Value Analysis of Closed Chains	p. 147
4.5.6 Application to General Networks	p. 149
4.6 BCMP Networks	p. 150
4.6.1 Overview of BCMP Networks	p. 150
4.6.2 Single Node--Exponential Server	p. 151
4.6.3 Single Node--Infinite Server	p. 152
4.6.4 Single Node--Processor Sharing	p. 156
4.6.5 Single Node--Last Come First Served (LCFS)	p. 158
4.7 Networks of BCMP Queues	p. 161
4.7.1 Store-and-Forward Message-Switched Nodes	p. 163
4.7.2 Example: Window Flow Control--A Closed Network Model	p. 170
4.7.3 Cellular Radio	p. 175
References	p. 178
Exercises	p. 179
5 Markov Chains: Application to Multiplexing and Access	p. 187
5.1 Time-Division Multiplexing	p. 187
5.2 The Arrival Process	p. 188
5.2.1 Packetization	p. 188
5.2.2 Compound Arrivals	p. 189
5.3 Asynchronous Time-Division Multiplexing	p. 190
5.3.1 Finite Buffer	p. 192
5.3.2 Infinite Buffer	p. 195
5.4 Synchronous Time-Division Multiplexing	p. 197
5.4.1 Application of Rouche's Theorem	p. 199
5.4.2 Calculations Involving Rouche's Theorem	p. 201
5.4.3 Message Delay	p. 203
5.5 Random Access Techniques	p. 207
5.5.1 Introduction to ALOHA	p. 207
5.5.2 Analysis of Delay	p. 210
References	p. 215
Exercises	p. 216
6 The M/G/1 Queue: Imbedded Markov Chains	p. 219
6.1 The M/G/1 Queue	p. 219
6.1.1 Imbedded Markov Chains	p. 220
6.1.2 Distribution of Message Delay: FCFS	p. 222
6.1.3 Residual Life Distribution: Alternate Derivation of the Pollaczek-Khinchin Formula	p. 231
6.1.4 Variation for the Initiator of a Busy Period	p. 234
6.1.5 Busy Period of the M/G/1 Queue	p. 237
6.2 The G/M/1 Queue	p. 241
6.3 Priority Queues	p. 244
6.3.1 Preemptive Resume Discipline	p. 245
6.3.2 L-Priority Classes	p. 252
6.3.3 Nonpreemptive Priorities	p. 256
6.4 Polling	p. 265
6.4.1 Basic Model: Applications	p. 265
6.4.2 Average Cycle Time	p. 267
6.4.3 Average Delay: Exhaustive, Gated, and Limited Service	p. 267
References	p. 274
Exercises	p. 275
7 Fluid Flow Analysis	p. 281
7.1 On-Off Sources	p. 281
7.1.1 Single Source	p. 281
7.1.2 Multiple Sources	p. 284
7.2 Infinite Buffers	p. 286
7.2.1 The Differential Equation for Buffer Occupancy	p. 286
7.2.2 Derivation of Eigenvalues	p. 289
7.2.3 Derivation of the Eigenvectors	p. 292
7.2.4 Derivation of Coefficients	p. 295
7.3 Finite Buffers	p. 298
7.4 More General Sources	p. 300
7.5 Analysis: Leaky Bucket	p. 300
7.6 Equivalent Bandwidth	p. 303
7.7 Long-Range-Dependent Traffic	p. 304
7.7.1 Definitions	p. 304
7.7.2 A Matching Technique for LRD Traffic Using the Fluid Flow Model	p. 306
References	p. 309
Exercises	p. 310
8 The Matrix Geometric Techniques	p. 313
8.1 Introduction	p. 313
8.2 Arrival Processes	p. 313
8.2.1 The Markov Modulated Poisson Process (MMPP)	p. 314
8.2.2 The Batch Markov Arrival Process	p. 316
8.2.3 Further Extensions	p. 319
8.2.4 Solutions of Forward Equation for the Arrival Process	p. 319
8.3 Imbedded Markov Chain Analysis	p. 321
8.3.1 Revisiting the M/G/1 Queue	p. 321
8.3.2 The Multidimensional Case	p. 323
8.3.3 Application of Renewal Theory	p. 328
8.3.4 Moments at Message Departure	p. 334
8.3.5 Steady-State Queue Length at Arbitrary Points in Time	p. 335
8.3.6 Moments of the Queue Length at Arbitrary Points in Time	p. 336
8.3.7 Virtual Waiting Time	p. 336
8.4 A Matching Technique for LRD Traffic	p. 337
8.4.1 d MMPPs and Equivalents	p. 337
8.4.2 A Fitting Algorithm	p. 339
Appendix 8A Derivation of Several Basic Equations Used in Text	p. 343
Appendix 8B Derivation of Variance and Covariance Functions of Two-State MMPP	p. 347
References	p. 355
Exercises	p. 355
9 Monte Carlo Simulation	p. 359
9.1 Simulation and Statistics	p. 359
9.1.1 Introduction	p. 359
9.1.2 Sample Mean and Sample Variance	p. 359
9.1.3 Confidence Intervals	p. 361
9.1.4 Sample Sizes and Run Times	p. 362
9.1.5 Histograms	p. 364
9.1.6 Hypothesis Testing and the Chi-Square Test	p. 368
9.2 Random-Number Generation	p. 370
9.2.1 Pseudorandom Numbers	p. 370
9.2.2 Generation of Continuous Random Variables	p. 371
9.2.3 Discrete Random Variables--General Case	p. 375
9.2.4 Generating Specific Discrete Random Variables	p. 377
9.2.5 The Chi-Square Test Revisited	p. 379
9.3 Discrete-Event Simulation	p. 380
9.3.1 Time-Driven Simulation	p. 380
9.3.2 Event-Driven Simulation	p. 381
9.4 Variance Reduction Techniques	p. 382
9.4.1 Common Random-Number Technique	p. 383
9.4.2 Antithetic Variates	p. 384
9.4.3 Control Variates	p. 385
9.4.4 Importance Sampling	p. 386
References	p. 387
Exercises	p. 387
Index	p. 389

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