Simulation Modeling and Arena

Emphasizes a hands-on approach to learning statistical analysis and model building through the use of comprehensive examples, problems sets, and software applications

With a unique blend of theory and applications, Simulation Modeling and Arena®, Second Edition integrates coverage of statistical analysis and model building to emphasize the importance of both topics in simulation. Featuring introductory coverage on how simulation works and why it matters, the Second Edition expands coverage on static simulation and the applications of spreadsheets to perform simulation.

The new edition also introduces the use of the open source statistical package, R, for both performing statistical testing and fitting distributions. In addition, the models are presented in a clear and precise pseudo-code form, which aids in understanding and model communication. Simulation Modeling and Arena, Second Edition also features:

• Updated coverage of necessary statistical modeling concepts such as confidence interval construction, hypothesis testing, and parameter estimation
• Additional examples of the simulation clock within discrete event simulation modeling involving the mechanics of time advancement by hand simulation
• A guide to the Arena Run Controller, which features a debugging scenario
• New homework problems that cover a wider range of engineering applications in transportation, logistics, healthcare, and computer science
• A related website with an Instructor’s Solutions Manual, PowerPoint® slides, test bank questions, and data sets for each chapter  

Simulation Modeling and Arena, Second Edition is an ideal textbook for upper-undergraduate and graduate courses in modeling and simulation within statistics, mathematics, industrial and civil engineering, construction management, business, computer science, and other departments where simulation is practiced. The book is also an excellent reference for professionals interested in mathematical modeling, simulation, and Arena.

Preface xvii

Acknowledgments xix

Introduction xxi

1 Simulation Modeling 1

1.1 Simulation Modeling 1

1.2 Why Simulate? 2

1.3 Types of Computer Simulation 3

1.4 Descriptive or Prescriptive? 6

1.5 Randomness in Simulation 7

1.6 Simulation Languages 7

1.7 Simulation Methodology 8

1.8 Organization of the Book 14

Exercises 15

2 Generating Randomness in Simulation 17

2.1 Stochastic Simulation 17

2.2 Random Numbers 18

2.3 Random Number Generators 19

2.4 Testing Random Numbers 24

2.4.1 Distributional Tests 24

2.4.2 Testing Independence 33

2.5 Random Variates 37

2.5.1 Inverse Transform 37

2.5.2 Convolution 45

2.5.3 Acceptance/Rejection 46

2.5.4 Mixture Distributions, Truncated Distributions, and Shifted Random Variables 49

2.6 Summary 53

Exercises 53

3 Spreadsheet Simulation 61

3.1 Simulation in a Spreadsheet Environment 61

3.2 Useful Spreadsheet Functions and Methods 62

3.2.1 Using RAND() and RANDBETWEEN() 62

3.2.2 Using VLOOKUP() 65

3.2.3 Using Data Tables to Repeatedly Sample 66

3.2.4 Using VBA 68

3.3 Example Spreadsheet Simulations 69

3.3.1 Simple Monte Carlo Integration 69

3.3.2 The Classic News Vendor Inventory Problem 73

3.3.3 Simulating a Random Cash Flow 76

3.4 Introductory Statistical Concepts 79

3.4.1 Point Estimates and Confidence Intervals 79

3.4.2 Determining the Sample Size 80

3.5 Summary 85

Exercises 85

4 Introduction to Simulation in ArenaTM 95

4.1 Introduction 95

4.2 The ArenaTM Environment 96

4.3 Performing Simple Monte-Carlo Simulations using ArenaTM 98

4.3.1 Re-Doing Area Estimation with ArenaTM 99

4.3.2 Re-Doing the News Vendor Problem with ArenaTM 102

4.4 How the Discrete-Event Clock Works 105

4.5 Modeling a Simple Discrete-Event Dynamic System 109

4.5.1 A Drive through Pharmacy 109

4.5.2 Modeling the System 110

4.5.3 Implementing the Model in ArenaTM 112

4.5.4 Specify the Arrival Process 113

4.5.5 Specify the Resources 115

4.5.6 Specify the Process 116

4.5.7 Specify Run Parameters 117

4.5.8 Analyze the Results 119

4.6 Extending the Drive Through Pharmacy Model 122

4.7 Animating the Drive Through Pharmacy Model 125

4.8 Getting Help in ArenaTM 132

4.9 SIMAN and the Run Controller 134

4.9.1 SIMAN MOD and EXP Files 134

4.9.2 Using the Run Controller 138

4.10 How ArenaTM Manages Entities and Events 146

4.11 Summary 150

Exercises 151

5 Basic Process Modeling 163

5.1 Elements of Process-Oriented Simulation 163

5.2 Entities, Attributes, and Variables 164

5.3 Creating and Disposing of Entities 166

5.4 Defining Variables and Attributes 170

5.5 Processing Entities 175

5.6 Attributes, Variables, and some I/O 177

5.6.1 Modifying the Pharmacy Model 177

5.6.2 Using the ASSIGN Module 180

5.6.3 Using the READWRITE Module 182

5.6.4 Using the RECORD Module 186

5.6.5 Animating a Variable 187

5.6.6 Running the Model 189

5.7 Flow of Control in Arena 192

5.7.1 Logical and Probabilistic Conditions 192

5.7.2 Iterative Looping 197

5.7.3 Example: Iterative Looping, Expressions, and Sub-models 198

5.8 Batching and Separating Entities 213

5.8.1 Example: Tie-Dye T-Shirts 213

5.9 Summary 225

Exercises 227

6 Modeling Randomness in Simulation 235

6.1 Random Variables and Probability Distributions 235

6.2 Modeling with Discrete Distributions 240

6.3 Modeling with Continuous Distributions 242

6.4 Input Distribution Modeling 244

6.5 Fitting Discrete Distributions 245

6.5.1 Fitting a Poisson Distribution 246

6.5.2 Visualizing the Data 246

6.5.3 Statistical Analysis of the Data 250

6.5.4 Checking the Goodness of Fit of the Model 253

6.6 Fitting Continuous Distributions 257

6.6.1 Visualizing the Data 257

6.6.2 Statistically Summarize the Data 258

6.6.3 Hypothesizing and Testing a Distribution 260

6.6.4 Visualizing the Fit 266

6.7 Using the Input Analyzer 271

6.8 Additional Input Modeling Concepts 280

6.9 Modeling Randomness in ArenaTM 283

6.9.1 Conceptualizing the Model 284

6.9.2 Implementing the Model 285

6.10 Summary 297

Exercises 298

7 Analyzing Simulation Output 303

7.1 Types of Statistical Variables 304

7.2 Types of Simulation With Respect To Output Analysis 310

7.3 Analysis of Finite Horizon Simulations 311

7.3.1 Determining the Number of Replications 313

7.3.2 Finite Horizon Example 315

7.3.3 Sequential Sampling for Finite Horizon Simulations 323

7.4 Analysis of Infinite Horizon Simulations 326

7.4.1 Assessing the Effect of Initial Conditions 332

7.4.2 Performing the Method of Replication-Deletion 338

7.4.3 Looking for the Warm up Period in the Output Analyzer 341

7.4.4 The Method of Batch Means 354

7.4.5 Performing the Method of Batch Means 358

7.5 Comparing System Configurations 362

7.5.1 Comparing Two Systems 362

7.5.2 Analyzing Multiple Systems 382

7.6 Summary 395

Exercises 396

8 Modeling Queueing and Inventory Systems 405

8.1 Introduction 405

8.2 Single Line Queueing Stations 406

8.2.1 Queueing Notation 408

8.2.2 Little’s Formula 410

8.2.3 Deriving Formulas for Markovian Single Queue Systems 413

8.3 Examples and Applications of Queueing Analysis 419

8.3.1 Infinite Queue Examples 419

8.3.2 Finite Queue Examples 424

8.4 Non-Markovian Queues and Approximations 430

8.5 Simulating Single Queues in ArenaTM 431

8.5.1 Machine Interference Optimization Model 431

8.5.2 Using OptQuest1 on the Machine Interference Model 439

8.5.3 Modeling Balking and Reneging 443

8.6 Holding and Signaling Entities 450

8.6.1 Redoing the M/M/1 Model with HOLD/SIGNAL 451

8.7 Networks of Queueing Stations 456

8.7.1 STATION, ROUTE, and SEQUENCE Modules 461

8.8 Inventory Systems 469

8.8.1 Modeling an (r;Q) Inventory Control Policy 470

8.8.2 Modeling a MultiEchelon

Inventory System 481

8.9 Summary 487

Exercises 489

9 Entity Movement and Material Handling 507

9.1 Introduction 507

9.2 Resource Constrained Transfer 508

9.2.1 Implementing Resource Constrained Transfer 511

9.2.2 Animating Resource Constrained Transfer 518

9.3 Constrained Transfer with Transporters 520

9.3.1 Test and Repair Shop with Workers as Transporters 524

9.3.2 Animating Transporters 529

9.4 Modeling Systems with Conveyors 531

9.4.1 Test and Repair Shop with Conveyors 536

9.4.2 Animating Conveyors 541

9.4.3 Miscellaneous Issues in Conveyor Modeling 543

9.5 Modeling Guided Path Transporters 550

9.6 Summary 559

Exercises 560

10 Miscellaneous Topics in ArenaTM Modeling 567

10.1 Introduction 567

10.2 Non-stationary Processes 568

10.2.1 Thinning Method 572

10.2.2 Rate Inversion Method 572

10.3 Advanced Resource Modeling 576

10.3.1 Scheduled Capacity Changes 577

10.3.2 Calculating Utilization 585

10.3.3 Resource Failure Modeling 588

10.4 Tabulating Frequencies using the STATISTIC Module 591

10.5 Resource and Entity Costing 594

10.5.1 Resource Costing 594

10.5.2 Entity Costing 598

10.6 Miscellaneous Modeling Concepts 602

10.6.1 Picking Between Stations 603

10.6.2 Generic Station Modeling 607

10.6.3 Picking up and Dropping Off Entities 612

10.7 Programming Concepts within ArenaTM 621

10.7.1 Using the Generated Access File 621

10.7.2 Working with Files, Excel, and Access 626

10.7.3 Using Visual Basic for Applications 639

10.7.4 Generating Correlated Random Variates 652

10.8 Summary 655

Exercises 656

11 Application of Simulation Modeling 663

11.1 Introduction 663

11.2 SM Testing Contest Problem Description 665

11.3 Answering the Basic Modeling Questions 671

11.4 Detailed Modeling 676

11.4.1 Conveyor and Station Modeling 676

11.4.2 Modeling Samples and the Test Cells 679

11.4.3 Modeling Sample Holders and the Load/Unload Area 685

11.4.4 Performance Measure Modeling 688

11.4.5 Simulation Horizon and Run Parameters 690

11.4.6 Preliminary Experimental Analysis 693

11.5 Final Experimental Analysis and Results 694

11.5.1 Using the Process Analyzer on the Problem 695

11.5.2 Using OptQuest on the Problem 701

11.5.3 Investigating the New Logic Alternative 702

11.6 Sensitivity Analysis 703

11.7 Completing the Project 704

11.8 Some Final Thoughts 707

Exercises 709

A Common Distributions 717

B Statistical Tables 725

C Distributions, Operators, Functions in ArenaTM 731

D Queueing Theory Formulas 735

E Inventory Theory Formulas 739

F Useful Equations 742

G ArenaTM Panel Modules 743

Index 749

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