livro simulation modeling and analysis

7/30/2019 Livro Simulation Modeling and Analysis

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Simulation Modelingand A nalysisT H I R D E D I T I O N

Averill M. LawPresidentAverill M. Law & Associates, Inc.Tucson, Arizona, USAwww . averill-law. com

W. David KeltonProfessorDepartment of Quantitative Analysis and Operations ManagementCollege of Business AdministrationUniversity ofCincinnatiCincinnati, Ohio, USAwww . econqa. cba. uc . edu/~keltond

Boston Burr Ridge, IL Dubuque, IA Madison, WlNew York San Francisco St. LouisBangkok Bogota Caracas Lisbon London Madrid Mex ico CityMilan New Delhi Seoul Singapore Sydney Taipei Toronto


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C O N T E N T S

List of Sym bols xviiPreface xixChapter 1 Basic Simulation M odeling 1

1.1 The Nature of Simulation 11.2 Systems, Models, and Simulation 31.3 Discrete-Event Simulation 61.3.1 Time-Advance Mechanisms 71.3.2 Components and Organization of a Discrete-EventSimulation Model 91.4 Simulation of a Single-Server Queueing System 121.4.1 Problem Statement 121.4.2 Intuitive Explanation 181.4.3 Program Organization and Logic 271.4.4 FORTRAN Program 321.4.5 C Program 411.4.6 Simulation Output and Discussion 491.4.7 Alternative Stopping Rules 511.4.8 Determining the Events and Variables 571.5 Simulation of an Inventory System 601.5.1 Problem Statement 601.5.2 Program Organization and Logic 621.5.3 FORTRAN Program 661.5.4 C Program 731.5.5 Simulation Output and Discussion 781.6 Alternative Approaches to Modeling and Coding Simulations 801.6.1 Parallel and Distributed Simulation 801.6.2 Simulation across the Internet and Web-BasedSimulation 831.7 Steps in a Sound Simulation Study 831.8 Other Types of Simulation 871.8.1 Continuous Simulation 87


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1.8.2 Combined Discrete-Continuous Simulation 891.8.3 Monte Carlo Simulation 901.9 Advantages, Disadvantages, and Pitfalls of Simulation 91Appendix 1A: Fixed-Increment Time Advance 93Appendix 1B: A Primer on Queueing Systems 941B.1 Components of a Queueing System 95IB.2 Notation for Queueing Systems 95IB.3 Measures of Performance for Queueing Systems 96Problems 99

Chapter 2 M odeling Com plex Systems 1062.1 Introduction 1062.2 List Processing in Simulation 1072.2.1 Approaches to Storing Lists in a Computer 1072.2.2 Linked Storage Allocation 1082.3 A Simple Simulation Language: simlib 1142.4 Single-Server Queueing Simulation with simlib 1232.4.1 Problem Statement 1232.4.2 simlib Program 1232.4.3 Simulation Output and Discussion 1282.5 Time-Shared Computer Model 1292.5.1 Problem Statement 1292.5.2 simlib Program 1302.5.3 Simulation Output and Discussion 1382.6 Multiteller Bank with Jockeying 1412.6.1 Problem Statement 1412.6.2 simlib Program 1422.6.3 Simulation Output and Discussion 1522.7 Job-Shop Model 1552.7.1 Problem Statement 1552.7.2 simlib Program 1572.7.3 Simulation Output and Discussion 1682.8 Efficient Event-List Manipulation 170

Appendix 2A: C Code for simlib 171Problems 184Chapter 3 Simu lation Software 2023.1 Introduction 2023.2 Comparison of Simulation Packages with ProgrammingLanguages 2033.3 Classification of Simulation Software 2043.3.1 General-Purpose Versus Application-OrientedSimulation Packages 204


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3.3.2 Modeling Approaches 2053.3.3 Common Modeling Elements 2073.4 Desirable Software Features 2083.4.1 General Capabilities 2083.4.2 Hardw are and Software Requirements 2103.4.3 Animation and Dynamic Graphics 2103.4.4 Statistical Capabilities 2123.4.5 Customer Support and Documentation 2133.4.6 Output Reports and Graphics 2143.5 General-Purpose Simulation Packages 2153.5.1 Arena 2153.5.2 Extend 2193.5.3 Other General-Purpose Simulation Packages 2253.6 Object-Oriented Simulation 2273.6.1 M OD SIM III 2283.7 Exam ples of Application-Oriented Simulation Packages 233

Chapter 4 Rev iew of Bas ic Probab ility and Statistics 2354.1 Introduction 2354.2 Random Variables and Their Properties 2354.3 Simulation Output Data and Stochastic Processes 2474.4 Estimation of Means, Variances, and Correlations 2494.5 Conndence Intervals and Hypothesis Tests for the Mean 2534.6 The Strong Law of Large Numbers 2594.7 The Danger of Replacing a Probability Distribution byits Mean 260

Appendix 4A: Comm ents on Covariance-StationaryProcesses 260Problems 261

Chapter 5 Building Valid, Credible, and Appropriately DetailedSimulation M odels 2645.1 Introduction and Definitions 2645.2 Guidelines for Determining the Level of Model Detail 2675.3 Verification of Simulation Com puter Programs 2695.4 Techniques for Increasing Model Validity and Credibility 273

5.4.1 Collect High-Quality Information and Data on theSystem 2745.4.2 Interact with the Manager on a Regulr Basis 2755.4.3 Maintain an Assumptions Document and Perform aStructured Walk-Through 2765.4.4 Validate Components of the Model by UsingQuantitative Techniques 277


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5.4.5 Validate the Output from the OverallSimulation Model 2795.4.6 Animation 2825.5 M anagements Role in the Simulation Process 2825.6 Statistical Procedures for Com paring Real-WorldObservations and Simulation Output Data 2835.6.1 Inspection Approach 2835.6.2 Confidence-Interval Approach Based onIndependent Data 2875.6.3 Time-Series Approaches 289

Problems 290Chapter 6 Selecting Input Probab ility Distributions 292

6.1 Introduction 2926.2 Useful Probability Distributions 2986.2.1 Parameterization of Continuous Distributions 2986.2.2 Continuous Distributions 2996.2.3 Discrete Distributions 3186.2.4 Empirical Distributions 3186.3 Techniques for Assessing Sample Independence 3296.4 Activity I: Hypothesizing Fam ilies of Distributions 3326.4.1 Summary Statistics 3336.4.2 Histograms 3356.4.3 Quantile Summaries and Box Plots 3376.5 Activity II: Estimation of Parameters 3436.6 Activity III: Determining How Representativethe Fitted Distributions Are 3476.6.1 Heuristic Procedures 347

6.6.2 Goodness-of-Fit Tests 3566.7 The ExpertFit Software and an Extended Example 3706.8 Shifted and Truncated Distributions 3766.9 Bezier Distributions 3786.10 Specifying Multivariate Distributions, Correlations, andStochastic Processes 3786.10.1 Specifying Multivariate Distributions 3806.10.2 Specifying Arbitrary Marginal Distributions

and Correlations 3836.10.3 Specifying Stochastic Processes 3846.11 Selecting a Distribution in the Absence of Data 3866.12 Models of Arrival Processes 3896.12.1 Poisson Processes 3896.12.2 Nonstationary Poisson Processes 3906.12.3 BatchArrivals 3936.13 Assessing the Homogeneity of Different Data Sets 394


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Appendix 6A: Tables of MLEs for the Gamm a and BetaDistributions 395Problems 397Chapter 7 Ran dom -Num ber Generators 402

7.1 Introduction 4027.2 Linear Congruential Generators 4067.2.1 Mixed Generators 4097.2.2 Multiplicative Generators 4107.3 Other Kinds of Generators 4127.3.1 More General Congruences 4137.3.2 Composite Generators 4147.3.3 Tausworthe and Related Generators 4167.4 Testing Random -Number Generators 4177.4.1 Empirical Tests 4187.4.2 Theoretical Tests 4237.4.3 Some General Observations on Testing 426Appendix 7A: Portable Computer Codes for a PMM LCG 4277A.1 FORTRAN 428

7A.2 C 4307A.3 Obtaining Initial Seeds for the Streams 431Appendix 7B : Portable C Code for a Combined MRG 432Problems 435437437439440448451452459459460460461461464465466467468468468

Chapter 8 Generating Random Variates8.18.2

8.3

IntroductionGeneral Approaches to Generating Random Variates8.2.18.2.28.2.38.2.48.2.5

Inverse TransformCompositionConvolutionAcceptance-RejectionSpecial PropertiesGenerating Continuous Random Variates8.3.18.3.28.3.38.3.48.3.58.3.68.3.78.3.88.3.98.3.108.3.11

UniformExponentialm-ErlangGammaWeibullNormalLognormalBetaPearson Type VPearson Type VILog-Logistic


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8.3.12 Johnson Bounded 4688.3.13 Johnson Unbounded 4698.3.14 Bezier 4698.3.15 Triangulr 4698.3.16 Empirical Distributions 4708.4 Generating Discrete Random Variates 4718.4.1 Bernoulli 4728.4.2 Discrete Uniform 4728.4.3 Arbitrary Discrete Distribution 4728.4.4 Binomial 4778.4.5 Geometrie 4778.4.6 Negative Binomial 4778.4.7 Poisson 4788.5 Generating Random Vectors, Correlated Random Variates,and Stochastic Processes 4788.5.1 Using Conditional Distributions 4798.5.2 Multivariate Normal and Multivariate Lognormal 4808.5.3 Correlated Gamm a Random Variates 4818.5.4 Generating from Multivariate Families 4828.5.5 Generating Random Vectors with Arbitrarily

Specified Marginal Distributions and Correlations 4828.5.6 Generating Stochastic Processes 4838.6 Generating Arrival Processes 4848.6.1 Poisson Processes 4858.6.2 Nonstationary Poisson Processes 4858.6.3 BatchA rrivals 489Appendix 8A: Validity of the Acceptance-RejectionMethod 489Appendix 8B : Setup for the Alias Method 490Problems 491

Chapter 9 Ou tput Da ta A nalysis for a Single System 4969.1 Introduction 4969.2 Transient and Steady-State Behavior of a Stochastic Process 4999.3 Types of Simulations with Regard to Output Analysis 5029.4 Statistical Analysis for Terminating Simulations 505

9.4.1 Estimating Means 5069.4.2 Estimating Other Measures of Performance 5159.4.3 Choosing Initial Conditions 5189.5 Statistical Analysis for Steady-State Parameters 5189.5.1 The Problem of the Initial Transient 5199.5.2 Replication/Deletion Approaches for Means 5259.5.3 Other Approaches for Means 5279.5.4 Estimating Other Measures of Performance 537


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9.6 Statistical Analysis for Steady-State Cycle Parameters 5399.7 Multiple Measures of Performance 5429.8 Time Plots of Important Variables 545Appendix 9A: Ratios of Expectations and JackknifeEstimators 545Problems 547

Chapter 10 Co m paring Alternative Sys tem Configurations 55310.1 Introduction 55310.2 Confidence Intervals for the Difference Between theExpected Responses of Two Systems 557

10.2.1 A Paired-f Confidence Interval 55710.2.2 A Modified Two-Sample-i Confidence Interval 55910.2.3 Contrasting the Two Methods 56010.2.4 Comparisons Based on Steady-State Measures ofPerformance 56010.3 Confidence Intervals for Com paring More thanTwo Systems 56210.3.1 Comparisons with a Standard 56310.3.2 All Pairwise Comparisons 56410.3.3 Multiple Comparisons with the Best 56610.4 Ranking and Selection 56610.4.1 Selecting the Best of k Systems 56710.4.2 Selecting a Subset of Size m Containing theBest of k Systems 56910.4.3 Selecting the m Best of k Systems 57010.4.4 Additional Problems and Methods 572Appendix 10A: Validity of the Selection Procedures 575Appendix 1 OB: Constants for the Selection Procedures 576Problems 579

Chapter 11 Va riance-Reduction Techn iques 58111.1 Introduction 58111.2 Common Random Num bers 58211.2.1 Rationale 58311.2.2 Applicability 584

11.2.3 Synchronization 58611.2.4 Som eExamp les 59011.3 Antithetic Variates 59811.4 Control Variates 60411.5 Indirect Estimation 61111.6 Conditioning 613Problems 617


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XVI CONTENTS

Chapter 12 Experimental Design, Sensitivity Analysis, andOptimization 62212.1 Introduction 62212.2 2k Factorial Designs 62512.3 Coping with Many Factors 63712.3.1 2k~p Fractional Factorial Designs 63812.3.2 Factor-Screening Strategies 64412.4 Response Surfaces and Metamodels 64612.5 Sensitivity and Gradient Estimation 65512.6 Optimum Seeking 65712.6.1 Optimum -Seeking Methods 659

12.6.2 Optimum-Seeking Packages Interfaced withSimulation Software 662Problems 666

Chapter 13 Sim ulation of M anufacturing System s 66913.1 Introduction 66913.2 Objectives of Simulation in Manufacturing 67013.3 Simulation Software for Manufacturing

Applications 67213.4 Modeling System Randomness 67513.4.1 Sources of Randomness 67513.4.2 Machine Downtimes 67813.5 An Extended Example 68413.5.1 Problem Description and Simulation Results 68413.5.2 Statistical Calculations 69313.6 A Simulation Case Study of a Metal-Parts ManufacturingFacility 69513.6.1 Description of the System 69513.6.2 Overall Objectives and Issues to Be Investigated 69613.6.3 Development of the Model 69613.6.4 Model Verification and Validation 69713.6.5 Results of the Simulation Experiments 69913.6.6 Conclusions and Benefits 701Problems 702Appendix 707References 711Sub ject Ind ex 745

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