Crafts Of Simulation Programming

by E Jack Chen

Overview

Crafts of Simulation Programs is a collection of tools, techniques and theories required to develop and implement simulation models on a computer. This timely book provides the various skills and techniques needed in simulation programming with general-purpose languages. The topics range in difficulty, and several latest fields in simulation output analysis are covered such as samples sizes, order statistics, ranking and selection, comparison with a control, selection with constraints, etc.Presented in the format of research project reports, detailed descriptions, important concepts and techniques are introduced and developed. Each chapter is relatively self-contained and can be used as a study unit. Algorithms have detailed implementations in C and are readable by anyone who has done a little programming. Many chapters include simulation results. It is designed to impart to the readers the statistical techniques used in simulation. This book will prove to be invaluable not only to students and researchers in the fields of simulation programming, but also to teachers of this subject who will find this text useful as a supplement.

Product Details

ISBN-13:	9789814740173
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	05/20/2016
Pages:	304
Product dimensions:	6.30(w) x 9.20(h) x 0.80(d)

Table of Contents

Preface vii

1 Basic Simulation Programming 1

1.1 Introduction 1

1.2 Random Numbers Generators 1

1.2.1 Basic Generators 4

1.2.2 The Need for Multiple Substreams 5

1.2.3 Computing (a × s) mod m 6

1.2.4 Computing the Jumping Matrices 6

1.2.5 A Random Number Package 7

1.2.6 Jumping Backward 9

1.3 Examples of Using Random Number Generator 10

1.4 Nonuniform Random Variates 13

1.4.1 Random Variates of Various Distributions 14

1.4.2 Correlated Random Variates 18

1.5 Utilities 20

1.5.1 Numerical Approximation of Normal Distribution 20

1.5.2 Quantile of Normal Distribution 21

1.5.3 Quantile of t Distribution 22

1.5.4 Quantile of Chi-square Distribution 23

1.5.5 Standard Deviation 25

1.6 Summary 26

2 Sample Sizes and Stopping Rules 27

2.1 Definitions 30

2.2 Batch-Means Method 32

2.3 Determining the Simulation Run Length 33

2.3.1 The von Neumann Test of Independence 33

2.3.2 A Source Code of the von Neumann Test 33

2.3.3 The Runs Test of Independence 34

2.3.4 A Source Code of Runs Up Test 36

2.3.5 An Implementation of Determining the Simulation Run Length 38

2.4 Constructing the Confidence Interval 38

2.5 A Correlation Adjustment 39

2.6 An Implementation of Batch-Means Method 39

2.7 An Illustration of Allocated Sample Sizes 43

2.8 Empirical Experiments 43

2.8.1 Experiment 1 46

2.8.2 Experiment 2 47

2.8.3 Experiment 3 48

2.9 Summary 49

3 Generating Independent and Identically Distributed Batch Means 51

3.1 Discussion of Batch-Means Method 51

3.2 Generating Independent and Normally Distributed Batch Means 52

3.2.1 Validation of Normality 52

3.2.2 A Source Code of Normality test 53

3.2.3 Batch Means Variance Estimator 54

3.2.4 The Implementation 56

3.2.5 Discussions of Batch-Means Procedures 58

3.3 Empirical Experiments 59

3.3.1 Experiment 1: Independence and Normality Tests 60

3.3.2 Experiment 2: Batch Sizes Determination 62

3.3.3 Experiment 3: Coverages of Confidence Interval 64

3.4 Summary 66

4 Distributions of Order Statistics 69

4.1 Joint and Conditional Distributions of Order Statistics 72

4.2 Using Range Statistics to Perform Equivalence Tests 74

4.2.1 Indifference-Zone Selection 74

4.2.2 Variance of Weighted Sample Means 75

4.2.3 Effects of the Indifference Amount and Sample Size 76

4.2.4 Equivalence Tests 77

4.2.5 Confidence Interval Half Width of Interest 79

4.3 Statistical Analysis of the Range 80

4.3.1 Simulating the Sample Range 81

4.3.2 Estimating Quantiles of the Range 82

4.4 Empirical Experiments 84

4.5 Summary 85

5 Order Statistics from Correlated Normal Random Variables 87

5.1 Order Statistics of Correlated Random Variables 88

5.1.1 Method of Evaluation of the Percentage Points 89

5.2 Applications of Correlated Order Statistics 90

5.2.1 Multiple Comparisons with a Control 90

5.2.2 Multiple Decision (Ranking and Selection) 92

5.2.3 Multiple Comparisons with a Control: Unknown Equal Variances 92

5.2.4 Multiple Comparisons with a Control: Unknown Unequal Variances 93

5.3 Empirical Experiments 94

5.3.1 Experiment 1: Known Equal Variances 94

5.3.2 Experiment 2: Unknown Equal Variances 95

5.3.3 Experiment 3: Unknown Unequal Variances 95

5.4 Summary 97

6 Histogram and Quasi-Independent Procedure 99

6.1 Introduction and Definitions 101

6.1.1 The Natural Estimators 103

6.1.2 Proportion Estimation 104

6.1.3 Quantile Estimation 105

6.2 Methodologies 106

6.2.1 Determining the Simulation Run Length 106

6.2.2 Histogram Approximation 106

6.2.3 Two-Phase Quantile Estimation 110

6.2.4 A Source Code of Quantile Estimation 113

6.3 Empirical Experiments 120

6.3.1 Independent Sequences 120

6.3.2 Correlated Sequences 122

6.3.3 A Practical Application 125

6.4 Summary 127

7 Metamodels 129

7.1 Introduction 129

7.2 Constructing Metamodels of Quantiles 131

7.3 Constructing Quantile Confidence Interval 133

7.4 Empirical experiments 133

7.4.1 Choosing the Design Points 133

7.4.2 Estimating Quantiles of Moving-Average and Autoregressive Processes via Non-functional-form Metamodels 134

7.4.3 Estimating Quantiles of Queuing Systems via Nonfunctional-form Metamodels 136

7.5 Summary 138

8 Density Estimation 141

8.1 Theoretical Basis 142

8.1.1 Empirical Distribution Functions 142

8.1.2 The Density Estimator 144

8.1.3 The Complication of Lack of Independence 146

8.2 An Implementation 146

8.2.1 Determine the Bandwidth 147

8.2.1 Determine the Sample Size 148

8.2.2 Density Confidence Interval 149

8.2.3 The Density-Estimation Procedure 150

8.3 Empirical Experiments 151

8.4 Summary 157

9 Comparing Two Alternatives 161

9.1 Background 161

9.1.1 Inference Procedures of Two Means 161

9.1.2 Null Hypothesis Tests of Equivalence 163

9.2 Methodology 164

9.2.1 A Weighted-Sample-Means Approach 164

9.2.2 Fix the Value of β = α/2 of Null Hypothesis Tests 165

9.3 Empirical Experiments 167

9.3.1 Experiment 1: Difference of Means 167

9.3.2 Experiment 2: Null Hypothesis of Equal Means 169

9.4 Summary 170

10 Ranking and Selection 171

10.1 Introduction 172

10.1.1 Generalized Subset Selection 172

10.1.2 Order Statistics of Continuous Distributions 173

10.1.3 A Review of Confidence Interval Half Width 175

10.1.4 Confidence Interval Half Width of Interest 176

10.1.5 Adjustment of the Difference of Sample Means 177

10.1.6 The Source Code of Computing Additional Sample Size 179

10.1.7 A Sequential Ranking and Selection Procedure (SRS) 180

10.2 Some Extensions of Selection of Continuous Distributions 182

10.2.1 Restricted Subset Selection 182

10.2.2 An Indifference-Zone Procedure to Select Only and/or All The Best Systems 183

10.2.3 Ratio Statistics of Variance of Normally Distributed Variables 186

10.2.4 Multiple Comparisons with the Best 190

10.3 Lognormally Distributed Samples 191

10.3.1 The Property of the Constant h_L 192

10.4 Other Approach of Selection Procedures 195

10.5 Empirical Experiments 196

10.5.1 Experiment 1: Normal Populations 196

10.5.2 Experiment 2: Exponential Populations 197

10.5.3 Experiment 3: Lognormal Populations 197

10.6 Summary 199

11 Computing Budget Allocation of Selection Procedures 201

11.1 Problem Statement 202

11.2 A Heuristic Computing Budget Allocation Rule 203

11.2.1 Confidence Interval Half-Width and Computing Budget 207

11.2.2 Maximizing Probability of Correction Selection with a Given Computing Budget 209

11.2.3 Optimal Computing Budget Allocation (OCBA) 211

11.3 Empirical Experiments 212

11.3.1 Experiment 1 Equal Variances 213

11.3.2 Experiment 2 Increasing Variances 214

11.3.3 Experiment 3 Decreasing Variances 216

11.4 Summary 216

12 Using Common Random Numbers with Selection Procedures 219

12.1 Common Random Numbers 219

12.2 The Basis of Correlated Order Statistics 220

12.2.1 Using CRNs with Dudewicz and Dalal's Procedure 220

12.2.2 Subset Selection with CRN 222

12.3 Empirical Experiments 225

12.3.1 Experiment 1: All Systems are Correlated 225

12.3.2 Experiment 2: Best System is Independent with Others 226

12.3.3 Experiment 3: Best System is Negatively Correlated with Others 229

12.3.4 Experiment 4: Unequal Variances 229

12.3.5 Experiment 5: Subset Selection - All Systems are Correlated 231

12.3.6 Experiment 6: Subset Selection - Independence Between Groups 1 233

12.3.7 Experiment 7: Subset Selection - Independence Between Groups 2 233

12.3.8 Experiment 8: Subset Selection - Unequal Variances 233

12.4 Summary 236

13 Parallel and Distributed Simulation 237

13.1 Introduction 237

13.2 Parallel and Distributed Selection 238

13.3 The Framework 240

13.4 Selection with All Pairwise Comparisons 241

13.5 Empirical Experiments 243

13.6 Summary 245

14 Multi-Objective Selection 247

14.1 Introduction 248

14.1.1 A Multi-Objective Selection Procedure 249 I

14.2 Methodologies 250

14.2.1 Prolog 250

14.2.2 The Strategy 251

14.2.3 The Incomplete Pareto Set Selection Procedure 252

14.2.4 The Two-Stage Pareto Set Selection Procedure 253

14.2.5 Incorporating Indifference-Zone 254

14.3 Empirical Experiments 255

14.3.1 Experiment 1: The Parameter m_p = 2 255

14.3.2 Experiment 2: The Parameter m_p = 3 256

14.3.3 Experiment 3: The Parameter m_p = 3 257

14.4 Summary 257

15 Generic Selection with Constraints 261

15.1 Methodologies 262

15.1.1 Multi-Objective Selection 262

15.1.2 A Generic Selection-With-Constraints Procedure 263

15.1.3 Variance as the Constraint 266

15.1.4 Variance as the Primary Performance Measure 267

15.2 Empirical Experiments 268

15.2.1 Selection With Constraints 268

15.2.2 Variance as the Constraint 270

15.2.3 Variance as the Primary Performance Measure 271

15.3 Summary 274

Appendix A Tables of Critical Constants 275

Bibliography 277

Index 285