SECOND EDITION SIMULATION MODELING ANALYSIS
SECONDEDITIONSIMULATIONMODELING&ANALYSISAverill M. LAw '! It 11W David ltonMeGRAW· HlllINTtRNATIONAL EDITIONSIn lUS1 " h gln ,ing So, .
McGraw-Hili Series in Industrial Engineering andManagement Science'Consulting EditorJames L. Riggs, Department of Industrial Engineering, Oregon State UniversityBarish and Kaplan: Economic Analysis: For Engineering and Managerial DecisionMakingBlank: Statistical Procedures for Engineering, Management, and ScienceCleland Kocaoglu: Engineering ManagementDenton: Safety Management: Improving PerformanceDervitsiotis: Operations ManagementGillet: Introduction to Operations Research: A Computer-oriented Algorithmic ApproachHicks: Introduction to Industrial Engineering and Management ScienceHuchingson: New Horizons for Human Factors in DesignLaw and Kelton: Simulation Modeling and AnalysisLeherer: White-Collar Productivity,Love: Inventory ControlNiebeJ, Draper and Wysk: Modern Manufacturing Process EngineeringPolk: Methods Analysis and Work MeasurementRiggs and West: Engineering EconomicsTaguchi, Eisayed and Hsiang: Quality Engineering in Production SystemsRiggs and West: Essentials of Engineering EconomicsWu and Coppins: Linear Programming and Extensions
SIMULATIONMODELING ANDANALYSISSecond EditionAverill M. LawPresidentSimulation Modeling and Analysis CompanyTucson, Arizona·Professor of Decision SciencesUniversi w.of ArizonaDavid KeltonAssociate Professor of Operations and Management ScienceCurtis L. Carlson School of ManagementUniversity of MinnesotaMcGraw·HiII, InC.New York St. Louis San Francisco Auckland Bogota Caracas HamburgLisbon London Madrid Mexico Milan Montreal New Delhi ParisSan Juan Sao Paulo Singapore ;Sydney Tokyo Toronto
SIMULATION MODELING AND ANALYSISInternational Editions 1991Exclusive rights by McGraw-Hill Book Co. - Singapore for manufacture andexport. This book cannot be re-exported from the country to which it is consignedby McGraw-Hili. 1991,198'2 by McGraw-Hili. Inc. All rights reserved.Except as pennitted under the United States Copyright Act of 1976, no partofthis pUblication may be reproduced or distributed in any fonn or by anymeans, or stored in a data base or retrieval system, without the prior writtenpermission oftbe publisher.Copyright890CWPFC9871bis book was set in Times Roman.The editors were Eric M. Munson and Matgery Luhrs.The production supervisor was Louise Karam.The cover was -designed by Ed Butler.Library of Congress Cataloging-in-PubUcatJon DataLaw. Averill M. Simulation modeling and analysis/Averill M. Law, W. DavidKelton. - 2nd ed.p.em. - (McGraw-Hill series in industrial engineering andmanagement science)Includes bibliographical references and index.ISBN 0-07-036698-51. Digital computer simulation.I. Kelton. W. Dav:id.II. TitleIII. Series . QA76.9.C65L381991003'.3 - dc20When ordering this title. use ISBN 0-07-100803-9Printed in Singapore90-42969
ABOUT THE AUTHORSAverlll M. Law is President of Simulation Modeling and Analysis Company ,(Tucson, Arizona), and Professor of Decision Sciences at the University ofArizona. He has been a simulation consultant to such organizations as GeneralMotors, IBM, AT&T, General Electric, 3M, Nabisco, Xerox, Kimberly-Clark,NASA, the Army, the Navy, and the Air Force. He has presented more than160 simulation seminars in 10 countries . He is the author (or coauthor) of four books and numerous papers onsimulation, manufacturing, operations research, and statistics. His article,"Statistical Analysis of Simulation Output Data," was the first invited featurepaper on simulation to appear in a major research journal. He won the 1988Institute of Industrial Engineers' best publication award for his series of paperson the simulation of manufacturing systems. He is the codeveloper of theUniFit II software package for fitting probability distributions to observeddata, and he developed a four-hour videotape on simulation with the Societyfor Manufacturing Engineers. Dr. Law writes a regular column on simulationfor Industrial Engineering magazine.He was preViously Associate Professor of Industrial Enginering at theUniversity of Wisconsin. Dr. Law has a Ph.D. in Industrial Engineering andOperations Research from the University of California at Berkeley.W. David Kelton is Associate Professor of Operations and ManagementScience in the Curtis L. Carlson School of Management at the University ofMinnesota, in Minneapolis, where he teaches courses on simulation, stochasticprocesses, statistics, and computing. He received a B.A. in Mathematics fromthe University of Wisconsin-Madison, an M.S. in Mathematics from OhioUniversity, as well as M.S. and Ph.D. degrees in Industrial Engineering fromthe University of Wisconsin. His research interests include the design andanalysis of simulation experiments, applied stochastic processes, and statisticalquality control. He serves as Associate Editor for Operations Research and IIETransactions, and is Simulation Area Editor for the ORSA Journal on Computv
viABOUT THE AUTHORSing; he is also President of The Institute for Management Sciences College onSimulation. In 1987 he served as Program Chair for the Winter SimulationConference, and is General Chair for this conference in 1991. He has consultedwith private industry, government, and nonprofit organizations on simulationand related topics.
To my wife, Steffi, and children, Heather, Adam, and Brian,for their encouragement and understandingduring the writing of this book.Averill M. LawFor Christie, Molly, and Anna.W. David Kelton
CONTENTSList of SymbolsPreface to the Second EditionPreface to the First Edition" Chapter 1 Basic Simulation Modelingjl.l:; 1.2./ 1.31137The Nature of SimulationSystems, rvIodels, and SimulationDiscrete-Event Simulation' ,1.3.11.3.2J1.4Time-Advance MechanismsComponents and 'Organization of a Discrete-EventSimulation ModelSimulation of a Single-Server Queueing System1.4.1 Problem .5 ,1.61.71.8Intuitive Explanation.Program Organization and LogicFORTRAN ProgramPascal ProgramC ProgramSimulation Output and Discu·ssionAlternative Stopping Rules . .Determining 'the Events and VariablesSimulation of an Inventory System1.5.1 'Problem Statement1.5.2 Program Organization and Logic1.5.3 FORTRAN Program1.5.4 Pascal Program1.5.5 C Program1.5.6 Simulation Output arid DiscussionDistributed SimulationSteps in a Simtilaiion StudyOther Types of 28996102103106109ix
XCONTENTS1.91.8.1 Continuous Simulation1.8.2 Combined Discrete-Continuous Simulation1.8.3 Monte Carlo SimulationAdvantages, Disadvantages, and Pitfalls of Simulation109112113114Appendix 1A: Fixed-Increment Time AdvanceAppendix lB: A Primer on Queueing SystemslB.1 Components of a Queueing System1B.2 Notation for Queueing Systems1B.3 Measures of Performance for Queueing SystemsAppendix 1C: Notes on the Computers and ter 2 Modeling Complex ionList Processing in Simulation2.2.1 Approaches to Storing Lists in a Computer2.2.2 Linked Storage AllocationA Simple Simulation Language, SIMLIBSingle-Server Queueing Simulation with SIMLIB2.4.1 Problem Statement2.4.2 SIMLIB Program2.4.3 Simulation Output and DiscussionTime-Shared Computer Model2.5.1· Problem Statement2.5.2 SIMLIB Program2.5.3. Simulation Output and Discussion.,Multiteller Bank with Jockeying2.6.1 Problem Statement2.6.2 SIMLIB Program.2.6.3 Simulation Output and DiscussionJob-Shop Model2.7.1 Problem Statement2.7.2 SIMLIB Program2.7.3 Simulation Output and Disc1\ssionEfficient Event-List 9170170171183185185187199200Appendix 2A:ProblemsReferences202-215232FORTRAN Code for SrMLIBChapter 3 Simulation SoftwareJJ122123130IntroductionComparison of Simulation Languages.with General-Purpose Languages .234234235
CONTENTS./ 3.3V 3.4Classification of Simulation SoftwareSimulation Languages vs. Simulators3.3.13.3.23.3.3Modeling. ApproachesCommon Modeling ElementsDesirable Software Features3.4.1 General Features3.4.2 Animation3.4.3 Statistical Capabilities3.4.4 Customer Support3.4.5 Output Reports3.5GPSS3.5.1 GPSS/H3.5.2 Simulation of the M I M 11 Queue3.5.3 . GPSS/PC.; 3.6SIMAN I Cinema. 3.6.1 Simulation of the M I M 11 Queue3.7SIMSCRIPT II.53.7.1 Simulation of the M I M 11 Queue3.8SLAM II and Related Software3.8.1 Simulation of the M I M 11 Queue3.9Comparison of Simulation Languages3.10 Additional Simulation SoftwareVVReferencesChapter 44.14.24.34.44.54.64.7Review of Basic Probability andStatisticsIntroductionRandom Variables and Their PropertiesSimulation Output Data and Stochastic Pr:ocessesEstimation of Means, Variances, and CorrelationsConfidence Intervals and Hypothesis Tests for the MeanThe Strong Law of Large NumbersThe Danger of Replacing a Probability Distributionby Its MeanAppendix 266267267268279282286292292Comments on Covariance-Station:aryProblemsChapter 5xiBuilding Valid and Credible SimulationModelsIntroduction and DefinitionsSome Principles of Valid Simulation ModelingVerification of Simulation Computer ProgramsGeneral Perspectives on Validation293294297298298300302306
xiiCONTENTS5.55.6A Three-Step Approach for Developing Valid and CredibleSimulation Models5.5.1 Develop a Model with High Face Valiaity5.5.2 Test the Assumptions of the Model Empirically5.5.3 Determine How Representative the SimulationOutput Data AreStatistical Procedures for Comparing Real-WorldObservations and Simulation Output Data5.6.15.6.2.'. -Inspection ApproachConfidence-Interval Approach Based onIndependent Data5.6.3 Time-Series ApproachesProblemsReferencesChapter 6 Selecting Input Probability Pistributions6.16.26.36.46.56.6IntroductionUseful Probability Distributions6.2.1 Parameteriza ion of Continuous Distributions6.2.2 Continuous Distributioris'6.2.3 Discrete Di.st.rlbutions·6.2.4 Empirical DistributionsTechniques for Assessing Sample IndependenceActivity I: Hypothesizing Families of Distributions6.4.1 Summary Statistics6.4.2 Histograms and Line Graphs6.4.3 Quantile Summaries and Box PlotsActivity II: Estimation of ParametersActivity III: Determining How Representative' theFitted Distributions Are6.6.1 Heuristic Procedures6.6.2 Goodness-of-Fit TestsAn Extended ExampleShifted and Truncated DistributionsSelecting a Distribution in the Absence of Data6.76.86.96.10Models of Arrival Processes6.11.6.10.1 Poisson .-Processes6.10.2 Nonstationary Poisson Processes6.10.3 Batch ArrivalsAssessing the Homogeneity of Different Data SetsAppendix 6A:Tables of MLEs lor the Gamma andBeta 409409411Problems413References417Chapter 7 Random-Number Generators7.1307308310Introduction420420
COmENTS7.27.37.4Linear Congruential GeneratorsMixed GeneratorsMultiplicative Generators7.2.17.2.2Other7.3.17.3.27.3.3More General CongruencesComposite GeneratorsTausworthe and Related GeneratorsTesting Random-Number Generators7.4.17.4.27.4.37.57.6Kinds of GeneratorsEmpirical TestsTheoretical TestsSome General Observations on TestingRandom-Number Generation on MicrocomputersGenerators Used by Simulation LanguagesAppendix 7A: Portable Computer Codes7A.1 FORTRAN7A.2 Pascal7A.3 C7A.4 Obtaining Initial Seeds for the StreamsProblemsReferencesChapter 88.18.2Generating Random VariatesIntroductionGeneral Approaclies to Generating Random Variates8.2.1Inverse .3.68.3.78.3.88.3.98.3.108.3.118.3.128.4Special PropertiesGenerating Continuous Random alLognormalBetaPearson Type VPearson Type VITriangularEmpirical DistributionsGenerating Discrete Random Variates8.4.18.4.28.4.3BernoulliDiscrete UniformArbitrary Discrete 7
egativ Binomial804.7PoissonGenerating Correlated Random Variates8.5.1Using Conditional Distributions8.5.2Multivariate Normal and Multivariate Lognormal8.5.3Correlated Gamma Random VariatesGenerating Arrival Processes8.6.1Poisson Processes8.6.28.6.3Nonstationary Poisson ProcessesBatch ArrivalsAppendix 8A:Appendix 8B:ProblemsReferencesChapter 99.19.29.39049.59.69.79.8Validity of the Acceptance-RejectionMethodSetup for the Alias MethodOutput Data Analysis for a Single SystemRatios of Expectations and JackknifeEstimatorsProblemsReferencesChapter 1010.110.2512513514518IntroductionTransient and Steady-State Behavior of a Stochastic ProcessTypes of Simulations with Regard to Output AnalysisStatistical Analysis for Terminating Simulations904.1 Estimating Means9.4.2 Estimating Other Measures of Performance9.4.3 Choosing Initial ConditionsStatistical Analysis for Steady-State Parameters9.5.1 The Problem of the Initial Transient9.5.2 Replication/Deletion Approach for Means9.5.3 Ollier Approaches for Means9.5.4 Estimating Other Measures of PerformanceStatistical Analysis for Steady-State Cycle Param.etersMultiple Measures of PerformanceTime Plots of Important VariablesAppendix 9A:502502502503504504505506507507507510Comparing Alternative SystemConfigurationsIntroductionConfidence Intervals for the Difference betweenPerformance Measures of Two Systems10.2.1 A Paired-t Confidence Interval522522525527532532540543544545 '551553564565568572572575579582582586587
CONlENTSXVA Modified Two-Sample-t Confidence IntervalContrasting the Two Methods588589Comparisons Based on Steady-State Measuresof PerformanceConfidence Intervals for Comparing More Than Two59010.2.210.2.310.20410.3lOASystems10.3.1 Comparisons with a Standard10.3.2 All Pairwise CompaiisonsRanking and Selection1004.1 Selecting the Best of k Systems1004.2 Selecting a Subset of Size m Containing the Bestof k Systems1004.3 ' Selecting the m Best of k Systems100404 . Additional Problems and Methods591592594595596Appendix lOA:Appendix lOB:ProblemsReferences604606607609Validity of the Selection ProceduresConstants for the Selection Procedures598600601Variance-Reduction Techniques61211.111.2IntroductionCommon Random Numbers11.2.1 Rationale11.2.2 Applicability11.2.3 Synchronization11.3Antithetic VariatesControl VariatesIndirect hapter 1111.204110411.511.6Some ExamplesProblemsReferencesChapter 12 Experimental Design and Optimization12.112.212.3120412.5Chapter 1313.113.2Introduction2k Factorial DesignsCoping with Many Factors12.3.1 2"P Fractional Factorial Designs12.3.2 Factor-Screening StrategiesResponse Surfaces and MetamodelsGradient EstimationProblemsReferencesSimulation of Manufacturing SystemsIntroductionObjectives of Simulation in 93696696697
xviCONTENTS13.313.413.513.6Simulation Software for Manufacturing ApplicationsModeling System Randomness13.4.1 Sources of Randomness13.4.2 Machine DowntimesAn Extended Example13.5.1 Problem Description and Simulation Results13.5.2 Statistical CalculationsA Simulation Case Study of'a Metal-Parts ManufacturingFacility.13.6.1 Description of the System'13;6.2 . Overall Objectives and, Issues to Be Investigated13.6.3 Development of the Model13.6.4 Model Verification and Validation13.6.5 Results of the Simulation Experiments13.6.6 Conclusions and BenefitsProblemsReferencesAppendixINDEXESAuthor IndexSubject 735737741743749
LIST OF SYMBOLSNotation orabbreviationAiAVATIlbBemoulli(p)beta(a,; a 2)bin(t, p)B(a" a,)B(t)CjjCjCorCovCPUCRNcvCVdd(n)dfDiDU(i, j)EOErlangexpo(f3)FIFOf(x)f(x, y)Page numberof definitionNotation orabbreviationPage number.of a, 9339341lIDLIFOLL(t)LN(Jt, (]"2)MIE2/1MIGIIMIMIIMIMI2MIMlsMLEN(Jt, (]"2)N(O, 1)negbin(s, p)p(x)p(x, y)POPareto( c, a 2)Poisson(A)PT5(a, (3)PT6(a, (3)xvii
xviiiLIST OF SYMBOLSNotation orabbreviationPage numberof definitionQQ(t)(s, 613333751206162,64262363276350282546287tn -t,t-aI2T(n)triang(a, b, c)UU(a, b)U(O,I)VarOVRTWeibull(a, (3)w.p.Ww(n)w(n)W,XqX O. 5Xci).,f(n)Y,(w)Zt-a!2Notation orabbreviationXk"":"l,l-a[(a)AA(t)A(I)IL" J (z)'1'(&)PpjjPj(T(T2'"(A""E.-- ( )LxJrxl{}Page numberof 9280278277119319,5871528719343370345344597268
PREFACE TO THE SECOND EDITIONWhile the general philosophy and organization of the First Edition have beenretained , the text has been almost completely rewritten. Our primary reasonsfor doing such a major revision were to bring the material up to date ; toimprove exposition and clarity, especially for the introductory material; and toemphasize the practical utility of the more advanced techniques treated in thelater chapters. There is one completely new chapter on manufacturing systems(Chap. 13), and the material on validation (formerly Chap. 10) has beenmoved forward (now Chap . 5) to emphasize that this activity must begin earlyin a simulation project. The numbers of examples , figures , and problems havebeen greatly expanded. A comprehensive Solutions Manual is available fromthe publisher.Several specific features of the Second Edition should be mentioned. Atthe beginning of each chapter we suggest particular sections that we feel arefundamental for all readers. A list of symbols and abbreviations has also beenadded. The computer programs in Chaps. 1 and 2 have been rewritten to useFORTRAN 77, and we have added complete Pascal and C versions of thesimulations in Chap. 1. (Chapter numbers henceforth refer to the SecondEdition.) The material on simulation languages in Chap. 3 has been updatedand now includes a discussion of animation . The review material in Chap . 4 hasbeen expanded to make it more accessible. Chapter 5 has been updated toreflect current thinking on validation, and emphasizes practical methods.Chapter 6 has many extended examples to illustrate the difficult task ofinput-distribution specification. Chapter 7, on random-number generators , hasbeen updated, and includes in App. 7A highly portable codes (in FORTRAN ,Pascal, and C) for a reliable generator. Chapter 8 contains expanded explanations of variate-generation methods, emphasizing graphical aids for enhancinginsight. Chapter 9 gives an updated and practically oriented discussion ofoutput analysis. Chapters 10 through 12 have been updated and rewritten toenhance development of intuition , and include many detailed examples of theuse of statistical comparison and ranking procedures, variance-reduction techniques , and experimental-design methodology. The new chapter (Chap. 13)xix
xxPREFACE TO TIlE SECOND EDmONdiscusses simulation applications to manufacturing systems, including relevantsoftware and several comprehensive examples! case studies.We have received valuable input from a large number of people andorganizations in preparing this major revision. The second author receivedsubstantial support from the University of Minnesota, especially the Department of Operations and Management Science, the Carlson School of Management, and Academic Computing Services; he is also grateful to the MinnesotaSupercomputer Institute for computational support. Special personal thanks goto Michael McComas and Stephen Vincent for numerous contributionsthroughout the book, and to Tom Schriber for his detailed reading of much ofthe manuscript. Knowing that we will almost surely commit grievous errors ofomission, we would nonetheless like to thank the following individuals for thei
5.6.3 Time-Series Approaches Problems References Selecting Input Probability Pistributions Introduction Useful Probability Distributions 6.2.1 Parameteriza ion of Continuous Distributions 6.2.2 Continuous Distributioris' 6.2.3 Discrete Di.st.rlbutions· 6.2.4 Empirical D
1 Simulation Modeling 1 2 Generating Randomness in Simulation 17 3 Spreadsheet Simulation 63 4 Introduction to Simulation in Arena 97 5 Basic Process Modeling 163 6 Modeling Randomness in Simulation 233 7 Analyzing Simulation Output 299 8 Modeling Queuing and Inventory Systems 393 9 Entity Movement and Material-Handling Constructs 489
RP 2K, Second Edition RP 2L, Third Edition RP 2M, First Edition Bul 2N, First Edition RP 2P, Second Edition RP 2Q, Second Edition RP 2R, First Edition RP 2T, First Edition Bul 2U, First Edition Bul 2V, First Edition Spec 2W, First Edition RP 2X, First Edition, with Supp 1 Spec 2Y, First Edition
Structural equation modeling Item response theory analysis Growth modeling Latent class analysis Latent transition analysis (Hidden Markov modeling) Growth mixture modeling Survival analysis Missing data modeling Multilevel analysis Complex survey data analysis Bayesian analysis Causal inference Bengt Muthen & Linda Muth en Mplus Modeling 9 .
Simulation modeling methodology research and simulation analysis methodology research have evolved into two near-ly separate fields. In this paper, ways are shown how simu-lation might benefit from modeling and analysis becoming more closely integrated. The thesis of this paper is that si-mulation analysis and simulation modeling methodologies,
CS445: Basic Simulation Modeling!!! Travis Desell!! Averill M. Law, Simulation Modeling & Analysis, Chapter 1. What is Simulation? A simulation uses a computer (or computers) to evaluate a model numerically, and data are gathered in order to estimate the desired true characteristics of the model. 1.
Modeling and Arena MANUEL D. ROSSETTI University of Arkansas WILEY John Wiley & Sons, Inc. Table of Contents 1 Simulation Modeling 1.1 Why Simulate? 2 1.2 Types of Computer Simulation 3 1.3 How the Discrete-Event Clock Works 5 1.4 Randomness in Simulation 9 1.5 Simulation Languages 9
ior and achieving simulation of the behavior in real time. Categories and Subject Descriptors: I.6.5 [Simulation and Modeling]: Model Development— Modeling methodologies General Terms: Simulation, Graphics, Dust Additional Key Words and Phrases: Physically-based Modeling, Real-time Simulation, Vehicle, Particle Systems, Computational Fluid .
Modeling and simulation modeling . 5 Formulas that are good for expressing static dependencies between variables, fail to work when it comes to describing the systems with dynamic behavior. This is the time for another modeling technology that is specifically designed for analyzing dynamic systems, namely for . simulation modeling. The .
