Simulation Modeling and Analysis
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1 Simulation Modeling and Analysis FOURTH EDITION Averill M. Law President Averill M. Law & Associates, Inc. Tucson, Arizona, USA www. averill-law. com Boston Burr Ridge, IL Dubuque, IA New York San Francisco St. Louis Bangkok Bogota Caracas Kuala Lumpur Lisbon London Madrid Mexico City Milan Montreal New Delhi Santiago Seoul Singapore Sydney Taipei Toronto
2 CONTENTS List of Symbols Preface xv xvii Chapter 1 Basic Simulation Modeling The Nature of Simulation Systems, Models, and Simulation Discrete-Event Simulation Time-Advance Mechanisms Components and Organization of a Discrete-Event Simulation Model Simulation of a Single-Server Queueing System Problem Statement Intuitive Explanation Program Organization and Logic C Program Simulation Output and Discussion Alternative Stopping Rules Determining the Events and Variables Simulation of an Inventory System Problem Statement Program Organization and Logic C Program Simulation Output and Discussion Parallel/Distributed Simulation and the High Level Architecture Parallel Simulation Distributed Simulation and the High Level Architecture Steps in a Sound Simulation Study Other Types of Simulation Continuous Simulation Combined Discrete-Continuous Simulation Monte Carlo Simulation Spreadsheet Simulation 74
3 Vlll CONTENTS 1.9 Advantages, Disadvantages, and Pitfalls of Simulation 76 Appendix 1 A: Fixed-Increment Time Advance 78 Appendix IB: A Primer on Queueing Systems 79 1B.1 Components of a Queueing System 80 1B.2 Notation for Queueing Systems 80 IB.3 Measures of Performance for Queueing Systems Chapter 2 Modeling Complex Systems Introduction List Processing in Simulation Approaches to Storing Lists in a Computer Linked Storage Allocation A Simple Simulation Language: simlib Single-Server Queueing Simulation with simlib Problem Statement simlib Program Simulation Output and Discussion Time-Shared Computer Model Problem Statement simlib Program Simulation Output and Discussion Multiteller Bank With Jockeying Problem Statement simlib Program Simulation Output and Discussion Job-Shop Model Problem Statement simlib Program Simulation Output and Discussion Efficient Event-List Manipulation 155 Appendix 2A: C Code for simlib Chapter 3 Simulation Software Introduction Comparison of Simulation Packages with Programming Languages Classification of Simulation Software General-Purpose vs. Application-Oriented Simulation Packages 189
4 CONTENTS IX Modeling Approaches Common Modeling Elements 3.4 Desirable Software Features General Capabilities Hardware and Software Requirements Animation and Dynamic Graphics Statistical Capabilities Customer Support and Documentation Output Reports and Graphics 3.5 General-Purpose Simulation Packages Arena Extend Other General-Purpose Simulation Packages 3.6 Object-Oriented Simulation 3.7 Examples of Application-Oriented Simulation Packages j)ter 4 Review of Basic Probability and Statistics 4.1 Introduction 4.2 Random Variables and Their Properties 4.3 Simulation Output Data and Stochastic Processes 4.4 Estimation of Means, Variances, and Correlations 4.5 Confidence Intervals and Hypothesis Tests for the Mean 4.6 The Strong Law of Large Numbers 4.7 The Danger of Replacing a Probability Distribution by its Mean Appendix 4A: Comments on Covariance-Stationary Processes er 5 Building Valid, Credible, and Appropriately Detailed Simulation Models 5.1 Introduction and Definitions 5.2 Guidelines for Determining the Level of Model Detail 5.3 Verification of Simulation Computer Programs 5.4 Techniques for Increasing Model Validity and Credibility Collect High-Quality Information and Data on the System Interact with the Manager on a Regular Basis Maintain a Written Assumptions Document and Perform a Structured Walk-Through Validate Components of the Model by Using Quantitative Techniques
5 X CONTENTS Validate the Output from the Overall Simulation Model Animation 5.5 Management's Role in the Simulation Process 5.6 Statistical Procedures for Comparing Real-World Observations and Simulation Output Data Inspection Approach Confidence-Interval Approach Based on Independent Data Time-Series Approaches Other Approaches Chapter 6 Selecting Input Probability Distributions 6.1 Introduction 6.2 Useful Probability Distributions Parameterization of Continuous Distributions Continuous Distributions Discrete Distributions Empirical Distributions 6.3 Techniques for Assessing Sample Independence 6.4 Activity I: Hypothesizing Families of Distributions Summary Statistics Histograms Quantile Summaries and Box Plots 6.5 Activity II: Estimation of Parameters 6.6 Activity III: Determining How Representative the Fitted Distributions Are Heuristic Procedures Goodness-of-Fit Tests 6.7 The ExpertFit Software and an Extended Example 6.8 Shifted and Truncated Distributions 6.9 Bezier Distributions 6.10 Specifying Multivariate Distributions, Correlations, and Stochastic Processes Specifying Multivariate Distributions Specifying Arbitrary Marginal Distributions and Correlations Specifying Stochastic Processes 6.11 Selecting a Distribution in the Absence of Data 6.12 Models of Arrival Processes Poisson Processes Nonstationary Poisson Processes Batch Arrivals
6 CONTENTS XI 6.13 Assessing the Homogeneity of Different Data Sets Appendix 6A: Tables of MLEs for the Gamma and Beta Distributions Chapter 7 Random-Number Generators 7.1 Introduction 7.2 Linear Congruential Generators Mixed Generators Multiplicative Generators 7.3 Other Kinds of Generators More General Congruences Composite Generators Feedback Shift Register Generators 7.4 Testing Random-Number Generators Empirical Tests Theoretical Tests Some General Observations on Testing Appendix 7A: Appendix 7B: Portable C Code for a PMMLCG Portable C Code for a Combined MRG Chapter 8 Generating Random Variates 8.1 Introduction 8.2 General Approaches to Generating Random Variates Inverse Transform Composition Convolution Acceptance-Rejection Ratio of Uniforms Special Properties Generating Continuous Rando Uniform Exponential m-erlang Gamma Weibull Normal Lognormal Beta Pearson Type V Pearson Type VI Log-Logistic
7 Xll CONTENTS Johnson Bounded Johnson Unbounded Bezier Triangular Empirical Distributions Generating Discrete Random Variates Bernoulli Discrete Uniform Arbitrary Discrete Distribution Binomial Geometric Negative Binomial Poisson Generating Random Vectors, Correlated Random Variates, and Stochastic Processes Using Conditional Distributions Multivariate Normal and Multivariate Lognormal Correlated Gamma Random Variates Generating from Multivariate Families Generating Random Vectors with Arbitrarily Specified Marginal Distributions and Correlations Generating Stochastic Processes Generating Arrival Processes Poisson Processes Nonstationary Poisson Processes Batch Arrivals 477 Appendix 8A: Validity of the Acceptance-Rejection Method 477 Appendix 8B: Setup for the Alias Method Chapter 9 Output Data Analysis for a Single System Introduction Transient and Steady-State Behavior of a Stochastic Process Types of Simulations with Regard to Output Analysis Statistical Analysis for Terminating Simulations Estimating Means Estimating Other Measures of Performance Choosing Initial Conditions Statistical Analysis for Steady-State Parameters The Problem of the Initial Transient Replication/Deletion Approach for Means Other Approaches for Means Estimating Other Measures of Performance 533
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