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Chapter1 Basic Simulation Modeling 1

1.1 The Nature of Simulation 1

1.2 Systems,Models,and Simulation 3

1.3 Discrete-Event Simulation 6

1.3.1 Time-Advance Mechanisms 7

1.3.2 Components and Organization of a Discrete-event Simulation Model 9

1.4 Simulation of a Single-Server Queueing System 12

1.4.1 Problem Statement 12

List of Symbols 17

1.4.2 Intuitive Explanation 18

Preface 19

1.4.3 Program Organization and Logic 27

1.4.4 FORTRAN Program 32

1.4.5 C Program 41

1.4.6 Simulation Output and Discussion 49

1.4.7 Alternative Stopping Rules 51

1.4.8 Determining the Events and Variables 57

1.5.1 Problem Statement 60

1.5 Simulation of and Inventory System 60

1.5.2 Program Organization and Logic 62

1.5.3 FORTRAN Program 66

1.5.4 C Program 73

1.5.5 Simulation Output and Discussion 78

1.6 Alternative Approaches to Modeling and Coding Simulations 80

1.6.1 Parallel and Distributed Simulation 80

1.6.2 Simulation across the Internet and Web-Based Simulation 83

1.7 Steps in a Sound Simulation Study 83

1.8 Other Types of Simulation 87

1.8.1 Continuous Simulation 87

1.8.2 Combined Discrete-Continuous Simulation 89

1.8.3 monte Carlo Simulation 90

1.9 Advantages,Disadvantages,and Pitfalls of Simulation 91

Appendix 1A:Fixed-Increment Time Advance 93

Appendix 1B:A Primer on Queueing Systems 94

1B.2 Notation for Queueing Systems 95

1B.1 Components of a Queueing System 95

1B.3 Measures of Performance for Queueing Systems 96

Problems 99

Chapter2 Modeling Complex Systems 106

2.1 Introduction 106

2.2 List Processing in Simulation 107

2.2.1 Approaches to Storing Lists in a Computer 107

2.2.2 Linked Storage Allocation 108

2.3 A Simple Simulation Language:simlib 114

2.4.2 simlib Program 123

2.4 Single-Server Queueing Simulation with simlib 123

2.4.1 Problem Statement 123

2.4.3 Simulation Output and Discussion 128

2.5 Time-Shared Computer Model 129

2.5.1 Problem Statement 129

2.5.2 simlib Program 130

2.5.3 Simulation Output and Discussion 138

2.6.1 Problem Statement 141

2.6 Multiteller Bank with Jockeying 141

2.6.2 simlib Program 142

2.6.3 Simulation Output and Discussion 152

2.7 Job-Shop Model 155

2.7.1 Problem Statement 155

2.7.2 simlib Program 157

2.7.3 Simulation Output and Discussion 168

2.8 Efficient Event-List Manipulation 170

Appendix2A: C Code for simlib 171

Problems 184

Chapter3 Simulation Software 202

3.1 Introduction 202

3.2 Comparison of Simulation Packages with Programming Languages 203

3.3 Classification of Simulation Software 204

3.3.1 General-Purpose Versus Application-oriented Simulation Packages 204

3.3.2 Modeling Approaches 205

3.3.3 Common Modeling Elements 207

3.4.1 General Capabilities 208

3.4 Desirable Software Features 208

3.4.2 Hardware and Software Requirements 210

3.4.3 Animation and Dynamic Graphics 210

3.4.4 Statistical Capabilities 212

3.4.5 Customer Support and Documentation 213

3.4.6 Output Reports and Craphics 214

3.5 General-Purpose Simulation Packages 215

3.5.1 Arena 215

3.5.2 Extend 219

3.5.3 Other General-Purpose Simulation Packages 225

3.6 Object-Oriented Simulation 227

3.6.1 MODSIM III 228

3.7 Examples of Application-Oriented Simulation Packages 233

Chapter4 Review of Basic Probability and Statistics 235

4.1 Introduction 235

4.2 Random Variables and Their Properties 235

4.3 Simulation Output Data and Stochastic Processes 247

4.4 Estimation of Means,Variances,and Correlations 249

4.5 Confidence Intervals and Hypothesis Tests for the Mean 253

4.6 The Strong Law of Large Numbers 259

4.7 The Danger of Replacing a Probability Distribution by its Mean 260

Appendix4A:Comments on Covariance-Stationary Processes 260

Problems 261

Chapter5 Building Valid,Credible,and Appropriately Detailed Simulation Models 264

5.1 Introduction and Definitions 264

5.2 Guidelines for Determining the Level of Model Detail 267

5.3 Verification of Simulation Computer Programs 269

5.4 Techniques for Increasing Model Validity and Credibility 273

5.4.1 Collect High-Quality Information and Data on the System 274

5.4.2 Interact with the Manager on a Regular Basis 275

5.4.3 Maintain and Assumptions Document and Perform a Structured Walk-Through 276

5.4.4 Validate Components of the Model by Using Quantitative Techniques 277

5.4.5 Validate the Output from the Overall Simulation Model 279

5.4.6 Animation 282

5.5 Management s Role in the Simulation Process 282

5.6.1 Inspection Approach 283

5.6 Statistical Procedures for Comparing Real-World Observations and Simulation Output Data 283

5.6.2 Confidence-Interval Approach Based on Independent Data 287

5.6.3 Time-Series Approaches 289

Problems 290

Chapter6 Selecting Input Probability Distributions 292

6.1 Introduction 292

6.2 Useful Probability Distributions 298

6.2.1 Parameterization of Continuous Distributions 298

6.2.2 Continuous Distributions 299

6.2.3 Discrete Distributions 318

6.2.4 Empirical Distributions 318

6.3 Techniques for Assessing Sample Independence 329

6.4 Activity Ⅰ:Hypothesizing Families of Distributions 332

6.4.1 Summary Statistics 333

6.4.2 Histograms 335

6.4.3 Quantile Summaries and Box Plots 337

6.5 ActivityⅡ：Estimation of Parameters 343

6.6.1 Heuristic Procedures 347

6.6 ActivityⅢ:Determining How Representative the Fitted Distributions Are 347

6.6.2 Goodness-of-Fit Tests 356

6.7 The ExpertFit Software and an Extended Example 370

6.8 Shifted and Truncated Distributions 376

6.9 Bezier Distributions 378

6.10 Specifying Multivariate Distributions,Correlations,and Stochastic Processes 378

6.10.1 Specifying Multivariate Distributions 380

6.10.2 Specifying Arbitrary Marginal Distributions and Correlations 383

6.10.3 Specifying Stochastic Processes 384

6.11 Selecting a Distribution in the Absence of Data 386

6.12 Models of Arrival Processes 389

6.12.1 Poisson Processes 389

6.12.2 Nonstationary Poisson Processes 390

6.12.3 Batch Arrivals 393

6.13 Assessing the Homogeneity of Different Data Sets 394

Appendix 6A:Tables of MLEs for the Gamma and Beta Distributions 395

Problems 397

Chapter7 Random-Number Generators 402

7.1 Introduction 402

7.2 Linear Congruential Generators 406

7.2.1 Mixed Generators 409

7.2.2 Multiplicative Generators 410

7.3 Other Kinds of Generators 412

7.3.1 More General Congruences 413

7.3.2 Composite Generators 414

7.3.3 Tausworthe and Related Generators 416

7.4 Testing Random-Number Generators 417

7.4.1 Empirical Tests 418

7.4.2 Theoretical Tests 423

7.4.3 Some General Observations on Testing 426

Appendix7A:Portable Computer Codes for a PMMLCG 427

7A.1 FORTRAN 428

7A.2 C 430

7A.3 Obtaining Initial Seeds for the Streams 431

Appendix 7B:Portable C Code for a Combined MRG 432

Problems 435

8.1 Introduction 437

Chapter8 Generating Random Variates 437

8.2 General Approaches to Generating Random Variates 439

8.2.1 Inverse Transform 440

8.2.2 Composition 448

8.2.3 Convolution 451

8.2.4 Acceptance-Rejection 452

8.2.5 Special Properties 459

8.3 Generating Continuous Random Variates 459

8.3.1 Uniform 460

8.3.2 Exponential 460

8.3.3 m-Erlang 461

8.3.4 Gamma 461

8.3.5 Weibull 464

8.3.6 Normal 465

8.3.7 Lognormal 466

8.3.8 Beta 467

8.3.12 Johnson Bounded 468

8.3.11 Log-Logistic 468

8.3.9 Pearson Type V 468

8.3.10 Pearson Type VI 468

8.3.13 Johnson Unbounded 469

8.3.14 Bezier 469

8.3.15 Triangular 469

8.3.16 Empirical Distributions 470

8.4 Generating Discrete Random Variates 471

8.4.2 Discrete Uniform 472

8.4.3 Arbitrary Discrete Distribution 472

8.4.1 Bernoulli 472

8.4.4 Binonial 477

8.4.5 Geometric 477

8.4.6 Negative Binomial 477

8.4.7 Poisson 478

8.5 Generating Random Vectors,Correlated Random Variates,and Stochastic Processes 478

8.5.1 Using Conditional Distributions 479

8.5.2 Multivariate Normal and Multivariate Lognormal 480

8.5.3 Correlated Gamma Random Variates 481

8.5.5 Generating Random Vectors with Arbitrarily Specified Marginal Distributions and Correlations 482

8.5.4 Generating from Multivariate Families 482

8.5.6 Generating Stochastic Processes 483

8.6 Generating Arrival Processes 484

8.6.1 Poisson Processes 485

8.6.2 Nonstationary Poisson Processes 485

8.6.3 Batch Arrivals 489

Appendix8A:Validity of the Acceptance-Rejection Method 489

Appendix8B:Setup for the Alias Method 490

Problems 491

9.1 Introduction 496

Chapter9 Output Data Analysis for a Single System 496

9.2 Transient and Steady-State Behavior of a Stochastic Process 499

9.3 Types of Simulations with Regard to Output Analysis 502

9.4 Statistical Analysis for Terminating Simulations 505

9.4.1 Estimating Means 506

9.4.2 Estimating Other Measures of Performance 515

9.4.3 Choosing Initial Conditions 518

9.5 Statistical Analysis for Steady-State Parameters 518

9.5.1 The Problem of the Initial Transient 519

9.5.2 Replicfation/Daletion Approaches for Means 525

9.5.3 Other Approaches for Means 527

9.5.4 Estimating Other Measures of Performance 537

9.6 Statistical Analysis for Steady-State Cycle Parameters 539

9.7 Multiple Measures of Performance 542

9.8 Time Plots of Important Variables 545

Appendix9A:Ratios of Expectations and Jackknife Estimators 545

Problems 547

10.1 Introduction 553

Chapter10 Comparing Alternative System Configurations 553

10.2 Confidence Intervals for the Difference Between the Expected Responses of Two Systems 557

10.2.1 A Paired-t Confidence Interval 557

10.2.2 A Modified Two-Sample-t Confidence Interval 559

10.2.3 Contrasting the Two Methods 560

10.2.4 Comparisons Based on Steady-State Measures of Performance 560

10.3 Confidence Intervals for Comparing More than Two Systems 562

10.3.1 Comparisons with a Standard 563

10.3.2 All Pairwise Comparisons 564

10.4 Ranking and Selection 566

10.3.3 Multiple Comparisons with the Best 566

10.4.2 Selecting a Subset of Size m Containing the Best of k Systems 569

10.4.3 Selecting the m Best of k Systems 570

10.4.4 Additional Problems and Methods 572

Appendix 10A:Validity of the Selection Procedures 575

Appendix 10B:Constants for the Selection Procedures 576

Problems 579

Chapter11 Variance-Reduction Techniques 581

11.1 Introduction 581

11.2 Common Random Numbers 582

11.2.1 Rationale 583

11.2.2 Applicability 584

11.2.3 Synchronization 586

11.2.4 Some Examples 590

10.4.1 Selecting the Best of k Systems 597

11.3 Antithetic Variates 598

11.4 Control Variates 604

11.5 Indirect Estimation 611

11.6 Conditioning 613

Problems 617

Chapter12 Experimental Design,Sensitivity Analysis,and Optimization 622

12.1 Introduction 622

12.2 2k Factorial Designs 625

12.3 Coping with Many Factors 637

12.3.1 2k-p Fractional Factorial Designs 638

12.3.2 Factor-Screening Strategies 644

12.4 Response Surfaces and Metamodels 646

12.5 Sensitivity and Gradient Estimation 655

12.6 Optimum Seeking 657

12.6.1 Optimum-Seeking Methods 659

12.6.2 Optimum-Seeking Packages Interfaced with Simulation Software 662

Problems 666

Chapter13 Simulation of Manufacturing Systems 669

13.1 Introduction 669

13.2 Objectives of Simulation in Manufacturing 670

13.3 Simulation Software for Manufacturing Applications 672

13.4 Modeling System Randomness 675

13.4.1 Sources of Randomness 675

13.4.2 Machine Downtimes 678

13.5 An Extended Example 684

13.5.1 Problem Description and Simulation Results 684

13.5.2 Statistical Calculations 693

13.6.1 Description of the System 695

13.6 A Simulation Case Study of a Metal-Parts Manufacturing Facility 695

13.6.2 Overall Objectives and Issues to Be Investigated 696

13.6.3 Development of the Model 696

13.6.4 Model Verification and Validation 697

13.6.5 Results of the Simulation Experiments 699

13.6.6 Conclusions and Benefits 701

Problems 702

Appendix 707

References 711

Subject Index 745