【下载】Markov Chains-Models, Algorithms and Applications~Wai-Ki.Ching.2006

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Markov Chains: Models, Algorithms and Applications (International Series in Operations Research & Management Science) (Hardcover)
Wai-Ki Ching (Author), Michael K. Ng (Author)


Editorial Reviews
Review
From the reviews:
"The authors outline recent developments of Markov chain models … . This book is aimed at students, professionals, practitioners, and researchers in scientific computing and operational research, who are interested in the formulation and computation of queuing and manufacturing systems. It gives a number of useful tools for researchers in real applications … ." (Alexander I. Zejfman, Zentralblatt MATH, Vol. 1089 (15), 2006)
"In this book’s … essential notions on Markov chains, hidden Markov models, and Markov decision processes are covered, with special emphasis on iterative methods for solving linear systems. … Each chapter finishes with a short summary and sometimes a selection of open problems. … This book is intended for students and researchers in applied mathematics, scientific computing, and operations research … . Overall, this book offers much interesting and up-to-date material on a wide variety of topics, dealing with finite-space Markov processes." (Jozef L. Teugels, Journal of the American Statistical Association, Vol. 103 (483), September, 2008)
Product Description
MARKOV CHAINS: Models, Algorithms and Applications outlines recent developments of Markov chain models for modeling queueing sequences, Internet, re-manufacturing systems, reverse logistics, inventory systems, bio-informatics, DNA sequences, genetic networks, data mining, and many other practical systems.
The book consists of eight chapters. Chapter 1 is a brief introduction to the classical theory on both discrete and continuous time Markov chains. The relationship between Markov chains of finite states and matrix theory is also discussed. Chapter 2 discusses the applications of continuous time Markov chains to model queueing systems and discrete time Markov chains for computing. Chapter 3 studies re-manufacturing systems and presents Markovian models for reverse manufacturing applications. In Chapter 4, Hidden Markov models are applied to classify customers. Chapter 5 discusses the Markov decision process for customer lifetime values. Customer Lifetime Values (CLV) is an important concept and quantity in marketing management. Chapter 6 covers higher-order Markov chain models. Multivariate Markov models are discussed in Chapter 7. It presents a class of multivariate Markov chain models with a lower order of model parameters. Chapter 8 studies higher-order hidden Markov models. It proposes a class of higher-order hidden Markov models with an efficient algorithm for solving the model parameters.
This book is aimed at students, professionals, practitioners, and researchers in applied mathematics, scientific computing, and operational research, who are interested in the formulation and computation of queueing and manufacturing systems.

Product Details Hardcover: 208 pages Publisher: Springer; 1 edition (December 5, 2005) Language: English ISBN-10: 0387293353 ISBN-13: 978-0387293356

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关键词：Applications Application Algorithms Algorithm Chains 下载 Applications Algorithms Markov Ching

Contents

1 Introduction 1

1.1 Markov Chains 1

1.1.1 Examples of Markov Chains 2

1.1.2 The nth-Step Transition Matrix 5

1.1.3 Irreducible Markov Chain and Classifications of States 7

1.1.4 An Analysis of the Random Walk 8

1.1.5 Simulation of Markov Chains with EXCEL 10

1.1.6 Building a Markov Chain Model11

1.1.7 Stationary Distribution of a Finite Markov Chain 14

1.1.8 Applications of the Stationary Distribution 16

1.2 Continuous Time Markov Chain Process 16

1.2.1 A Continuous Two-state Markov Chain 18

1.3 Iterative Methods for Solving Linear Systems 19

1.3.1 Some Results on Matrix Theory 20

1.3.2 Splitting of a Matrix 21

1.3.3 Classical Iterative Methods 22

1.3.4 Spectral Radius 24

1.3.5 Successive Over-Relaxation (SOR) Method 26

1.3.6 Conjugate Gradient Method 26

1.3.7 Toeplitz Matrices 30

1.4 Hidden Markov Models 32

1.5 Markov Decison Process 33

1.5.1 Stationary Policy 35

2 Queueing Systems and the Web 37

2.1 Markovian Queueing Systems 37

2.1.1 An M/M/1/n − 2 Queueing System 37

2.1.2 An M/M/s/n − s − 1 Queueing System 39

2.1.3 The Two-Queue Free System 41

2.1.4 The Two-Queue Overflow System 42

2.1.5 The Preconditioning of Complex Queueing Systems 43

2.2 Search Engines 47

2.2.1 The PageRank Algorithm 49

2.2.2 The Power Method 50

2.2.3 An Example 51

2.2.4 The SOR/JOR Method and the Hybrid Method 52

2.2.5 Convergence Analysis 54

2.3 Summary 58

3 Re-manufacturing Systems 61

3.1 Introduction 61

3.2 An Inventory Model for Returns 62

3.3 The Lateral Transshipment Model 66

3.4 The Hybrid Re-manufacturing Systems 68

3.4.1 The Hybrid System 69

3.4.2 The Generator Matrix of the System 69

3.4.3 The Direct Method 71

3.4.4 The Computational Cost 74

3.4.5 Some Special Cases Analysis 74

3.5 Summary 75

4 Hidden Markov Model for Customers Classification77

4.1 Introduction 77

4.1.1 A Simple Example77

4.2 Parameter Estimation 78

4.3 Extension of the Method 79

4.4 Special Case Analysis 80

4.5 Application to Classification of Customers 82

4.6 Summary 85

5 Markov Decision Process for Customer Lifetime Value 87

5.1 Introduction 87

5.2 Markov Chain Models for Customers’ Behavior 89

5.2.1 Estimation of the Transition Probabilities 90

5.2.2 Retention Probability and CLV 91

5.3 Stochastic Dynamic Programming Models 92

5.3.1 Infinite Horizon without Constraints 93

5.3.2 Finite Horizon with Hard Constraints 95

5.3.3 Infinite Horizon with Constraints 96

5.4 Higher-order Markov decision process 102

5.4.1 Stationary policy 103

5.4.2 Application to the calculation of CLV 105

5.5 Summary 106

6 Higher-order Markov Chains 111

6.1 Introduction 111

6.2 Higher-order Markov Chains 112

6.2.1 The New Model 113

6.2.2 Parameters Estimation 116

6.2.3 An Example 119

6.3 Some Applications 121

6.3.1 The DNA Sequence 122

6.3.2 The Sales Demand Data 124

6.3.3 Webpages Prediction126

6.4 Extension of the Model 129

6.5 Newboy’s Problems 134

6.5.1 A Markov Chain Model for the Newsboy’s Problem 135

6.5.2 A Numerical Example 138

6.6 Summary 139

7 Multivariate Markov Chains 141

7.1 Introduction 141

7.2 Construction of Multivariate Markov Chain Models 141

7.2.1 Estimations of Model Parameters 144

7.2.2 An Example 146

7.3 Applications to Multi-product Demand Estimation 148

7.4 Applications to Credit Rating 150

7.4.1 The Credit Transition Matrix 151

7.5 Applications to DNA Sequences Modeling 153

7.6 Applications to Genetic Networks 156

7.6.1 An Example 161

7.6.2 Fitness of the Model 163

7.7 Extension to Higher-order Multivariate Markov Chain 167

7.8 Summary 169

8 Hidden Markov Chains 171

8.1 Introduction 171

8.2 Higher-order HMMs 171

8.2.1 Problem 1 173

8.2.2 Problem 2 175

8.2.3 Problem 3 176

8.2.4 The EM Algorithm 178

8.2.5 Heuristic Method for Higher-order HMMs 179

8.2.6 Experimental Results 182

8.3 The Interactive Hidden Markov Model 183

8.3.1 An Example 183

8.3.2 Estimation of Parameters 184

8.3.3 Extension to the General Case 186

8.4 The Double Higher-order Hidden Markov Model 187

8.5 Summary 189

References 191

Index 203

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