Notation Precedence Diagram

Transcription

1 Notation Precedence Diagram xix xxi CHAPTER 1 Introduction Systems, Models, and Simulation Verification, Approximation, and Validation Verifying a Program Approximation and Validation States, Events, and Clocks Simulation Types and Examples Synchronous and Asynchronous Discrete-Event Simulation Continuous Simulation Hybrid Simulation Introduction to Random Numbers Perspective on Experimental Design and Estimation Clock Mechanisms Hints for Simulation Programming Miscellaneous Problems 34 CHAPTER 2 Variance Reduction Common Random Numbers Informal Approach Formal Development Auxiliary Results Antithetic Variates Control Variates 59

2 xiv 2.4. Stratification 2.5. Importance Sampling 2.6. Conditional Monte Carlo 2.7. Jackknifing CHAPTER 3 Output Analysis 3.1. Introduction Finite-Horizon Versus Steady-State Performance Fixed Sample Size Versus Sequential Sampling 3.2. Analysis of Finite-Horizon Performance Absolute Performance Estimation Relative Performance Estimation 3.3. Analysis of Steady-State Performance Batch Means Regenerative Methods Spectral Analysis Methods Autoregressive Methods Recommendations 3.4. Analysis of Transaction-Based Performance 3.5. Indirect Estimation via r = As 3.6. Problems 3.7. Renewal Theory Primer 3.8. Standardized Time Series Steady State Transients CHAPTER 4 Rational Choice of Input Distributions 4.1. Addition and the Normal Distribution 4.2. Multiplication and the Lognormal 4.3. Memorylessness and the Exponential 4.4. Superposition, the Poisson, and the Exponential 4.5. Minimization and the Weibull Distribution 4.6. A Mixed Empirical and Exponential Distribution 4.7. Extreme Values and Spacings 4.8. When Not to Use a Theoretical Distribution 4.9. Nonstationary Poisson Processes CHAPTER 5 Nonuniform Random Numbers 5.1. Introduction 5.2. General Methods Inversion Tabular Approximation of the Inverse Transform Empirical cdf's A Mixed Empirical and Exponential Distribution Rejection

3 xv Generalized Rejection Composition The Alias Method for Discrete Distributions Functional Approximations of the Inverse Transform Other Ingenious Methods Continuous Distributions The Nonstandard Normal Distribution The Multivariate (Dependent) Normal Distribution Symmetric Stable Variates The Cauchy Distribution The Lognormal Distribution The Exponential Distribution The Hyperexponential Distribution The Laplace and Exponential Power Distributions Erlang and Gamma Distributions The Beta Distribution The Chi-square Distribution The F-Distribution The t-distribution The Weibull Distribution The Gumbel Distribution The Logistic Distribution The Generalized Lambda Distribution Nonhomogeneous Poisson Processes Discrete Distributions The Binomial Distribution The Poisson Distribution Compound Poisson Distributions The Hypergeometric Distribution ; The Geometric Distribution The Negative Binomial and Pascal Distributions Multidimensional Poisson Distributions Problems Timings 189 CHAPTER 6 Uniform Random Numbers Random Introductory Remarks What Constitutes Randomness Classes of Generators Random Devices Tables The Midsquare Method Fibonacci and Additive CongruentialGenerators Linear Congruential Generators Linear Recursion mod 2 Generators Combinations of Generators Choosing a Good Generator Based on Theoretical Considerations Serial Correlation of Linear Congruential Generators 205

4 xvi Cycle Length of Linear Congruential Generators Cycle Length for Tausworthe Generators The Spectral Test Implementation of Uniform Random Number Generators Multiplicative Generator With Modulus 2" Multiplicative Generators With Prime Modulus Implementing the Tausworthe Generator Empirical Testing of Uniform Random Number Generators Chi-square Tests Kolmogorov-Smirnov Tests Tests Specifically for Uniform Random Number Sequences Proper Use of a Uniform Random Number Generator Generating Random Integers Uniform Over an Arbitrary Interval Nonrandomness in the Low-order Bits of Multiplicative Generators Linear Congruential Generators and the Box-Muller Method Exploiting Special Features of Uniform Generators Generating Antithetic Variates With a Multiplicative Congruential Generator Generating a Random Number Stream in Reverse Order Generating Disjoint Sequences 226 CHAPTER 7 Simulation Programming Simulation With General-Purpose Languages The Simplest Possible Clock Mechanism Generating Random Variates Data Structures in Fortran A Complete Simulation in Fortran Fortran Simulation Packages Our Standard Example the Naive Approach Simulation Using Pascal Simscript Data Structures in Simscript Simscript and Simulation A Complete Simulation in Simscript The Standard Example in Simscript Processes and Resources Summing-up GPSS The Basic Concepts Resources in GPSS Generating Random Variates A Complete Simulation in GPSS The Standard Example in GPSS Summing-up Simula The Class Concept in Simula Simulation Using System Classes and Procedures A Complete Simulation in Simula 269

5 xvii Demos The Standard Example in Simula With Demos Summing-up General Considerations in Simulation Programming Language Design System Considerations in Simulation Statistical Considerations 279 CHAPTER 8 Programming to Reduce the Variance Choosing an Input Distribution Using an Exact Method Inverting a Tabulated Distribution Using a Mixed Empirical and Exponential Distribution Testing Robustness Common Random Numbers Antithetic Variates Control Variates The Simple Approach Regression With Splitting Regression With Jackknifing Stratified Sampling Importance Sampling Conditional Monte Carlo Summary 300 APPENDIX A The Shapiro-Wilk Test for Normality 303 APPENDIX L Routines for Random Number Generation 306 APPENDIX X Examples of Simulation Programming 348 References 375 Author Index 389 Subject Index 393