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Probability and Statistics with Reliability, Queuing, and Computer Science Applications / Edition 2

Probability and Statistics with Reliability, Queuing, and Computer Science Applications / Edition 2

by Kishor S. Trivedi
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Product Details

ISBN-13: 9780471333418
Publisher: Wiley
Publication date: 11/28/2001
Edition description: REV
Pages: 848
Product dimensions: 6.40(w) x 9.50(h) x 1.60(d)

About the Author

Kishor S. Trivedi, PhD, is the Hudson Professor of Electrical and Computer Engineering at Duke University, Durham, North Carolina. His research interests are in reliability and performance assessment of computer and communication systems. Dr. Trivedi has published extensively in these fields, with more than 600 articles and three books to his name. Dr. Trivedi is a Fellow of the IEEE and a Golden Core Member of the IEEE Computer Society.

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Table of Contents

Preface to the Second Edition ix

Preface to the First Edition xi

Acronyms xiii

1 Introduction 1

1.1 Motivation 1

1.2 Probability Models 2

1.3 Sample Space 3

1.4 Events 6

1.5 Algebra of Events 7

1.6 Graphical Methods of Representing Events 11

1.7 Probability Axioms 13

1.8 Com binatorial Problems 19

1.9 Conditional Probability 23

1.10 Independence of Events 25

1.11 Bayes'Rule 38

1.12 Bernoulli Trials 45

2 Discrete Random Variables 61

2.1 Introduction 61

2.2 Random Variables and Their Event Spaces 62

2.3 The Probability Mass Function 64

2.4 Distribution Functions 66

2.5 Special Discrete Distributions 68

2.6 Analysis of Program MAX 92

2.7 The Probability Generating Function 96

2.8 Discrete Random Vectors 99

2.9 Independent Random Variables 104

3 Continuous Random Variables 115

3.1 Introduction 115

3.2 The Exponential Distribution 119

3.3 The Reliability and Failure Rate 124

3.4 Some Important Distributions 129

3.5 Functions of a Random Variable 148

3.6 Jointly Distributed Random Variables 153

3.7 Order Statistics 157

3.8 Distribution of Sums 167

3.9 Functions of Normal Random Variables 182

4 Expectation 193

4.1 Introduction 193

4.2 Moments 197

4.3 Expectation Based on Multiple Random Variables 200

4.4 Transform Methods 208

4.5 Moments and Transforms of Some Distributions 217

4.6 Computation of Mean Time to Failure 228

4.7 Inequalities and Limit Theorems 237

5 Conditional Distribution and Expectation 247

5.1 Introduction 247

5.2 Mixture Distributions 255

5.3 Conditional Expectation 262

5.4 Impefect Fault Coverage and Reliability 268

5.5 Random Sums 279

6 Stochastic Processes 289

6.1 Introduction 289

6.2 Classification of Stochastic Processes 294

6.3 The Bernoulli Process 300

6.4 The Poisson Process 304

6.5 Renewal Processes 314

6.6 Availability Analysis 319

6.7 Random Incidence 328

6.8 Renewal Model of Program Behavior 332

7 Discrete-Time Markov Chains 337

7.1 Introduction 337

7.2 Computation of n-step Transition Probabilities 341

7.3 State Classification and Limiting Probabilities 347

7.4 Distribution of Times Between State Changes 356

7.5 Markov Modulated Bernoulli Process 358

7.6 Irreducible Finite Chains with Aperiodic States 361

7.7 The MIG/l Queuing System 377

7.8 Discrete-Time Birth-Death Processes 385

7.9 Finite Markov Chains with Absorbing States 392

8 Continuous-Time Markov Chains 405

8.1 Introduction 405

8.2 The Birth- Death Process 412

8.3 Other Special Cases of the Birth-Death Model 446

8.4 Non-Birth-Death Processes 454

8.5 Markov Chains with Absorbing States 496

8.6 Solution Techniques 520

8.7 Automated Generation 530

9 Networks of Queues 555

9.1 Introduction 555

9.2 Open Queuing Networks 560

9.3 Closed Queuing Networks 568

9.4 General Service Distribution and Multiple Job Types 596

9.5 Non-product-form Networks 604

9.6 Computing Response Time Distribution 617

9.7 Summary 630

10 Statistical Inference 637

10.1 Introduction 637

10.2 Parameter Estimation 639

10.3 Hypothesis Testing 692

11 Regression and Analysis of Variance 727

11.1 Introduction 727

11.2 Least-squares Curve Fitting 732

11.3 The Coefficients of Determination 735

11.4 Confidence Intervals in Linear Regression 738

11.5 Trend Detection and Slope Estimation 742

11.6 Correlation Analysis 745

11.7 Simple Nonlinear Regression 748

11.8 Higher-dimensional Least-squares Fit 749

11.9 Analysis of Variance 751

A Bibliography 765

A.1 Theory 765

A.2 Applications 770

B Properties of Distributions 777

C Statistical Tables 780

D Laplace Transforms 801

E Program Performance Analysis 808

Author Index 811

Subject Index 819

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Probability and Statistics with Reliability, Queuing, and Computer Science Applications 5 out of 5 based on 0 ratings. 7 reviews.
Guest More than 1 year ago
This book from Prof. K. Trivedi is another great guide for the novice student and the expert researcher for modeling tools and techniques. It builds upon neatly explained concepts of probability, queuing and stochastic processes to provide a variety of examples of applications. It is definitely a book that one has to keep at hand, as it contains recipes for a huge number of performance and dependability evaluation needs. Besides the rich content, the structure and the presentation are great: a bit of theory and soon one example from practical life, the reader never gets lost but he is rather brought step by step to a comprehensive understanding of the topics
Guest More than 1 year ago
This book is a MUST READ for computer science students as well as for professionals in the field. It is especially useful for anyone working with communications, reliability and performance. The highlights of the book are the rich set of examples as well as the problems at the end of each section and chapter, used to demonstrate the application of the material to real world problems. Many other computer science and engineering books miss the mark here. The material encourages you to relate what you¿ve learned and how you see it applied, to the problems you are currently working on. I would highly recommend this book to computer professionals who are looking to increase their toolset for solving complex problems.
Guest More than 1 year ago
This is the long waited 2nd Edition of Trivedi¡¯s classic book on reliability and availability (R&A) analysis of computer and telecommunication systems. It is arguably the best single source book for gaining a comprehensive understanding of both the theories and the best practices of R&A analysis in computer and telecommunication systems. The book not only covers the theories (Markov chains, stochastic reward nets, fault trees, etc.) in detail, but also provides a wide range of real world examples in showing how to apply the theories. After reading the book, a reader would find it easy to start constructing analytical models for R&A analysis of computing systems. I would highly recommend this book as an excellent advanced undergraduate or graduate course textbook. If you are doing any kind of reliability, availability and performance analysis for computer, telecommunication, or mission-critical systems, you should buy this book as a reference.
Guest More than 1 year ago
for every engineer, teacher, student and practitioner delving in performance and reliability modeling. For those who already have the first edition, this second edition is an extremely worthwhile 'upgrade'. The new examples in modeling software-reliability and fault-tolerance reflect the state of the art in respective fields. The book not only contains extensive material for learning (and teaching as well) performance and reliability modeling, but also gives insight into tons of real-life modeling problems in software, systems networking etc. Much of it through simplified, easy to follow examples and problem sets. A comprehensive solutions manual is also available. This book will continue to be the 'gold standard' of the art of performance and reliability modeling much like the first edition was.
Guest More than 1 year ago
This book provides a comprehensive treatment of the subject in a very readable form. I particularly like the examples in every chapter that cover a wide range of applications including computer systems, computer networking, telecommunications, wireless systems and software reliability. The examples are current and are very helpful in exposing the mathematical concepts. As a professional working in the area of reliability and performance I consult this book frequently. If I were teaching a course on the subject this would be my first choice for a textbook.
Guest More than 1 year ago
It is perhaps the most comprehensive book on reliability, availability, and performability to date. Excellent for both beginners and veterans. Good for both academic teaching/research and practical engineering. Its depth and breadth and the ample examples it provides make it extraordinarily useful.
Guest More than 1 year ago
A comprehensive solution manual (405 pages) to the book is now available to instructors. Contact