Discrete-Event System Simulation FIFTH EDITION

Jerry Banks Technolgico de Monterrey, Campus Monterrey

John S. Carson II Independent Simulation Consultant

Barry L. Nelson Northwestern University

David M. Nicol University of Illinois, Urbana-Champaign

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Contents

Preface 11 What's New in the Fifth Edition 15 List of Materials Available on www.bcnn.net 16 About the Authors 17

I Introduction to Discrete-Event System Simulation 19

1 Introduction to Simulation 21

1.1 When Simulation Is the Appropriate Tool 22 1.2 When Simulation Is Not Appropriate 22 1.3 Advantages and Disadvantages of Simulation 23 1.4 Areas of Application 25 1.5 Some Recent Applications of Simulation 27 1.6 Systems and System Environment 30 1.7 Components of a System 30 1.8 Discrete and Continuous Systems 32 1.9 Model of a System 33 1.10 Types of Models 33 1.11 Discrete-Event System Simulation 34 1.12 Steps in a Simulation Study 34

References 39 Exercises 40

2 Simulation Examples in a Spreadsheet 42

2.1 The Basics of Spreadsheet Simulation 43 2.1.1 How to Simulate Randomness 43

4 Contents

2.1.2 The Random Generators Used in the Examples 45 2.1.3 How to Use the Spreadsheets 46 2.1.4 How to Simulate a Coin Toss 47 2.1.5 How to Simulate a Random Service Time 48 2.1.6 How to Simulate a Random Arrival Time 51 2.1.7 A Framework for Spreadsheet Simulation 53

2.2 A Coin Tossing Game 55 2.3 Queueing Simulation in a Spreadsheet 58

2.3.1 Waiting Line Models 59 2.3.2 Simulating a Single-Server Queue 63 2.3.3 Simulating a Queue with Two Servers 69

2.4 Inventory Simulation in a Spreadsheet 73 2.4.1 Simulating the News Dealer's Problem 75 2.4.2 Simulating an (M,N) Inventory Policy 79

2.5 Other Examples of Simulation 83 2.5.1 Simulation of a Reliability Problem 83 2.5.2 Simulation of Hitting a Target 86 2.5.3 Estimating the Distribution of Lead-Time Demand 89 2.5.4 Simulating an Activity Network 91

2.6 Summary 94 References 95 Exercises 96

3 General Principles 106

3.1 Concepts in Discrete-Event Simulation 107 3.1.1 The Event Scheduling/Time Advance Algorithm 110 3.1.2 WorldViews 114 3.1.3 Manual Simulation Using Event Scheduling 116

3.2 List Processing 126 3.2.1 Basic Properties and Operations Performed on Lists 127 3.2.2 Using Arrays for List Processing 128 3.2.3 Using Dynamic Allocation and Linked Lists 130 3.2.4 Advanced Techniques 132

3.3 Summary 132 References 133 Exercises 133

4 Simulation Software 135

4.1 History of Simulation Software 136 4.1.1 The Period of Search (1955-1960) 137 4.1.2 The Advent (1961-1965) 137 4.1.3 The Formative Period (1966-1970) 137 4.1.4 The Expansion Period (1971-1978) 138

Contents 5

4.1.5 The Period of Consolidation and Regeneration (1979-1986) 138 4.1.6 The Period of Integrated Environments (1987-2008) 139 4.1.7 The Future (2009-2011) 139

4.2 Selection of Simulation Software 140 4.3 An Example Simulation 144 4.4 Simulation in Java 144 4.5 Simulation in GPSS 155 4.6 Simulation in SSF 159 4.7 Simulation Environments 163

4.7.1 AnyLogic 164 4.7.2 Arena 165 4.7.3 AutoMod 166 4.7.4 Enterprise Dynamics 167 4.7.5 ExtendSim 167 4.7.6 Flexsim 168 4.7.7 ProModel 169 4.7.8 SIMUL8 169

4.8 Experimentation and Statistical-Analysis Tools 170 4.8.1 Common Features 170 4.8.2 Products 170 References 173 Exercises 174

II Mathematical and Statistical Models 187

5 Statistical Models in Simulation 189

5.1 Review of Terminology and Concepts 190 5.1.1 Di screte random variables 190 5.1.2 Continuous random variables 191 5.1.3 Cumulative distribution function 193 5.1.4 Expectation 195 5.1.5 The mode 197

5.2 Useful Statistical Models 197 5.2.1 Queueing systems 197 5.2.2 Inventory and supply-chain systems 200 5.2.3 Reliability and maintainability 201 5.2.4 Limited data 201 5.2.5 Other distributions 201

5.3 Discrete Distributions 201 5.3.1 Bernoulli trials and the Bernoulli distribution 201 5.3.2 Binomial distribution 202 5.3.3 Geometric and Negative Binomial distributions 204 5.3.4 Poisson distribution 205

6 Contents

5.4 Continuous Distributions 207 5.4.1 Uniform distribution 207 5.4.2 Exponential distribution 209 5.4.3 Gamma distribution 212 5.4.4 Erlang distribution 213 5.4.5 Normal distribution 215 5.4.6 Weibull distribution 222 5.4.7 Triangular distribution 224 5.4.8 Lognormal distribution 227 5.4.9 Beta distribution 228

5.5 Poisson Process 229 5.5.1 Properties of a Poisson Process 231 5.5.2 Nonstationary Poisson Process 232

5.6 Empirical Distributions 234 5.7 Summary 236

References 237 Exercises 237

6 Queueing Models 245 6.1 Characteristics of Queueing Systems 246

6.1.1 The Calling Population 247 6.1.2 System Capacity 240 6.1.3 The Arrival Process 248 6.1.4 Queue Behavior and Queue Discipline 250 6.1.5 Service Times and the Service Mechanism 250

6.2 Queueing Notation 252 6.3 Long-Run Measures of Performance of Queueing Systems 253

6.3.1 Time-Average Number in System L 253 6.3.2 Average Time Spent in System Per Customer w 255 6.3.3 The Conservation Equation: L = Xw 257 6.3.4 Server Utilization 258 6.3.5 Costs in Queueing Problems 268

6.4 Steady-State Behavior of Infinite-Population Markovian Models 265 6.4.1 Single-Server Queues with Poisson Arrivals and Unlimited Capacity: M/G/l 266 6.4.2 Multiserver Queue: M/M/c/oo/oo 271 6.4.3 Multiserver Queues with Poisson Arrivals and Limited Capacity: M/M/c/N /006

6.5 Steady-State Behavior of Finite-Population Models {M/M/c/K/K) 278 6.6 Networks of Queues 281 6.7 Rough-cut Modeling: An Illustration 283 6.8 Summary 285

References 286 Exercises 286

Contents 7

III Random Numbers 293

7 Random-Number Generation 295

7.1 Properties of Random Numbers 295 7.2 Generation of Pseudo-Random Numbers 296 7.3 Techniques for Generating Random Numbers 297

7.3.1 Linear Congruential Method 298 7.3.2 Combined Linear Congruential Generators 301 7.3.3 Random-Number Streams 303

7.4 Tests for Random Numbers 304 7.4.1 Frequency Tests 305 7.4.2 Tests for Autocorrelation 309

7.5 Summary 312 References 312 Exercises 313

8 Random-Variate Generation 317

8.1 Inverse-Transform Technique 318 8.1.1 Exponential Distribution 318 8.1.2 Uniform Distribution 321 8.1.3 WeibuII Distribution 323 8.1.4 Triangular Distribution 323 8.1.5 Empirical Continuous Distributions 324 8.1.6 Continuous Distributions without a Closed-Form Inverse 329 8.1.7 Discrete Distributions 330

8.2 Acceptance-Rejection Technique 332 8.2.1 Poisson Distribution 334 8.2.2 Nonstationary Poisson Process 339 8.2.3 Gamma Distribution 340

8.3 Special Properties 341 8.3.1 Direct Transformation for the Normal and Lognormal Distributions 342 8.3.2 Convolution Method 343 8.3.3 More Special Properties 345

8.4 Summary 345 References 345 Exercises 346

IV Analysis of Simulation Data 351

9 Input Modeling 353

9.1 Data Collection 354 9.2 Identifying the Distribution with Data 359

9.2.1 Histograms 359

Contents

9.2.2 Selecting the Family of Distributions 362 9.2.3 Quantile-Quantile Plots 365

9.3 Parameter Estimation 368 9.3.1 Preliminary Statistics: Sample Mean and Sample Variance 368 9.3.2 Suggested Estimators 370

9.4 Goodness-of-Fit Tests 376 9.4.1 Chi-Square Test 377 9.4.2 Chi-Square Test with Equal Probabilities 379 9.4.3 Kolmogorov-Smirnov Goodness-of-Fit Test 381 9.4.4 p-Values and "Best Fits" 383

9.5 Fitting a Nonstationary Poisson Process 384 9.6 Selecting Input Models without Data 385 9.7 Multivariate and Time-Series Input Models 387

9.7.1 Covariance and Correlation 388 9.7.2 Multivariate Input Models 388 9.7.3 Time-Series Input Models 390 9.7.4 The Normal-to-Anything Transformation 392

9.8 Summary 394 References 396 Exercises 397

10 Verification, Calibration, and Validation of Simulation Models 406

10.1 Model Building, Verification, and Validation 407 10.2 Verification of Simulation Models 408 10.3 Calibration and Validation of Models 413

10.3.1 Face Validity 414 10.3.2 Validation of Model Assumptions 415 10.3.3 Validating Input-Output Transformations 415 10.3.4 Input-Output Validation: Using Historical Input Data 4426 10.3.5 Input-Output Validation: Using a Turing Test 430

10.4 Summary 431 References 432 Exercises 433

11 Estimation of Absolute Performance 435

11.1 Types of Simulations with Respect to Output Analysis 436 11.2 Stochastic Nature of Output Data 439 11.3 Absolute Measures of Performance and Their Estimation 441

11.3.1 Point Estimation 441 11.3.2 Confidence-Interval Estimation 443

11.4 Output Analysis for Terminating Simulations 445 11.4.1 Statistical Background 445 11.4.2 Confidence Intervals with Specified Precision 449 11.4.3 Quantiles 451

Contents 9

11.4.4 Estimating Probabilities and Quantiles from Summary Data 452 11.5 Output Analysis for Steady-State Simulations 453

11.5.1 Initialization Bias in Steady-State Simulations 454 11.5.2 Error Estimation for Steady-State Simulation 458 11.5.3 Replication Method for Steady-State Simulations 462 11.5.4 Sample Size in Steady-State Simulations 466 11.5.5 Batch Means Method for Steady-State Simulations 467 11.5.6 Steady-State Quantiles 470

11.6 Summary 471 References 472 Exercises 473

12 Estimation of Relative Performance 481

12.1 Comparison of Two System Designs 482 12.1.1 Independent Sampling 485 12.1.2 Common Random Numbers (CRN) 486 12.1.3 Confidence Intervals with Specified Precision 492

12.2 Comparison of Several System Designs 493 12.2.1 Bonferroni Approach to Multiple Comparisons 494 12.2.2 Selection of the Best 496

12.3 Metamodeling 501 12.3.1 Simple Linear Regression 501 12.3.2 Metamodeling and Computer Simulation 507

12.4 Optimization via Simulation 509 12.4.1 What Does "Optimization via Simulation" Mean? 510 12.4.2 Why is Optimization via Simulation Difficult? 512 12.4.3 Using Robust Heuristics 513 12.4.4 An Illustration: Random Search 516

12.5 Summary 518 References 519 Exercises 520

V Applications 525

13 Simulation of Manufacturing and Material-Handling Systems 527

13.1 Manufacturing and Material-Handling Simulations 528 13.1.1 Models of Manufacturing Systems 528 13.1.2 Models of Material Handling Systems 530 13.1.3 Some Common Material-Handling Equipment 530

13.2 Goals and Performance Measures 532 13.3 Issues in Manufacturing and Material-Handling Simulations 533

13.3.1 Modeling Downtimes and Failures 533 13.3.2 Trace-Driven Models 537

10 Contents

13.4 Case Studies of the Simulation of Manufacturing and Material Handling 538 13.5 Manufacturing Example: An Assembly-line Simulation 541

13.5.1 System Description and Model Assumptions 541 13.5.2 Presimulation Analysis 544 13.5.3 Simulation Model and Analysis of the Designed System 545 13.5.4 Analysis of Station Utilization 545 13.5.5 Analysis of Potential System Improvements 546 13.5.6 Concluding Words: The Gizmo Assembly-Line Simulation 548

13.6 Summary 548 References 548 Exercises 549

14 Simulation of Networked Computer Systems 559

14.1 Introduction 560 14.2 Simulation Tools 562

14.2.1 Process Orientation 564 14.2.2 Event Orientation 566

14.3 Model Input 567 14.3.1 Modulated Poisson Process 568 14.3.2 Poisson-Pareto Process 569 14.3.3 Pareto-length Phase Time 573 14.3.4 WWW Traffic 575

14.4 Mobility Models in Wireless Systems 576 14.5 The OSI Stack Model 578 14.6 Physical Layer in Wireless Systems 580

14.6.1 Propagation Models 580 14.6.2 Determining the Receivers 586

14.7 Media Access Control 587 14.7.1 Token-Passing Protocols 587 14.7.2 Ethernet 591

14.8 Data Link Layer 593 14.9 TCP 594 14.10 Model Construction 601

14.10.1 Construction 601 14.10.2 DML Example 602

14.11 Summary 605 References 606 Exercises 607

Appendix 609

Index 625