A Guide to Simulation

1 Introduction.- 1.1. Systems, Models, and Simulation.- 1.2. Verification, Approximation, and Validation.- 1.2.1. Verifying a Program.- 1.2.2. Approximation and Validation.- 1.3. States, Events, and Clocks.- 1.4. Simulation-Types and Examples.- 1.4.1. Synchronous and Asynchronous Discrete-Event Simulation.- 1.4.2. Continuous Simulation.- 1.4.3. Hybrid Simulation.- 1.5. Introduction to Random Numbers.- 1.6. Perspective on Experimental Design and Estimation.- 1.7. Clock Mechanisms.- 1.8. Hints for Simulation Programming.- 1.9. Miscellaneous Problems.- 2 Variance Reduction.- 2.1. Common Random Numbers.- 2.1.1. Informal Approach.- 2.1.2. Formal Development.- 2.1.3. Auxiliary Results.- 2.2. Antithetic Variates.- 2.3. Control Variates.- 2.4. Stratification.- 2.5. Importance Sampling.- 2.6. Conditional Monte Carlo.- 2.7. Jackknifing.- 3 Output Analysis.- 3.1. Introduction.- 3.1.1. Finite-Horizon Versus Steady-State Performance.- 3.1.2. Fixed Sample Size Versus Sequential Sampling.- 3.2. Analysis of Finite-Horizon Performance.- 3.2.1. Absolute Performance Estimation.- 3.2.2. Relative Performance Estimation.- 3.3. Analysis of Steady-State Performance.- 3.3.1. Batch Means.- 3.3.2. Regenerative Methods.- 3.3.3. Spectral Analysis Methods.- 3.3.4. Autoregressive Methods.- 3.3.5. Recommendations.- 3.4. Analysis of Transaction-Based Performance.- 3.5. Indirect Estimation via r = ?s.- 3.6. Problems.- 3.7. Renewal Theory Primer.- 3.8. Standardized Time Series.- 3.8.1. Steady State.- 3.8.2. Transients.- 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.- 5 Nonuniform Random Numbers.- 5.1. Introduction.- 5.2. General Methods.- 5.2.1. Inversion.- 5.2.2. Tabular Approximation of the Inverse Transform.- 5.2.3. Empirical cdf's.- 5.2.4. A Mixed Empirical and Exponential Distribution.- 5.2.5. Rejection.- 5.2.6. Generalized Rejection.- 5.2.7. Composition.- 5.2.8. The Alias Method for Discrete Distributions.- 5.2.9. Functional Approximations of the Inverse Transform.- 5.2.10. Other Ingenious Methods.- 5.3. Continuous Distributions.- 5.3.1. The Nonstandard Normal Distribution.- 5.3.2. The Multivariate (Dependent) Normal Distribution.- 5.3.3. Symmetric Stable Variates.- 5.3.4. The Cauchy Distribution.- 5.3.5. The Lognormal Distribution.- 5.3.6. The Exponential Distribution.- 5.3.7. The Hyperexponential Distribution.- 5.3.8. The Laplace and Exponential Power Distributions.- 5.3.9. Erlang and Gamma Distributions.- 5.3.10. The Beta Distribution.- 5.3.11. The Chi-square Distribution.- 5.3.12. The F-Distribution.- 5.3.13. The t-Distribution.- 5.3.14. The Weibull Distribution.- 5.3.15. The Gumbel Distribution.- 5.3.16. The Logistic Distribution.- 5.3.17. The Generalized Lambda Distribution.- 5.3.18. Nonhomogeneous Poisson Processes.- 5.4. Discrete Distributions.- 5.4.1. The Binomial Distribution.- 5.4.2. The Poisson Distribution.- 5.4.3. Compound Poisson Distributions.- 5.4.4. The Hypergeometric Distribution.- 5.4.5. The Geometric Distribution.- 5.4.6. The Negative Binomial and Pascal Distributions.- 5.4.7. Multidimensional Poisson Distributions.- 5.5. Problems.- 5.6. Timings.- 6 Uniform Random Numbers.- 6.1. Random Introductory Remarks.- 6.2. What Constitutes Randomness.- 6.3. Classes of Generators.- 6.3.1. Random Devices.- 6.3.2. Tables.- 6.3.3. The Midsquare Method.- 6.3.4. Fibonacci and Additive Congruential Generators.- 6.3.5. Linear Congruential Generators.- 6.3.6. Linear Recursion mod 2 Generators.- 6.3.7. Combinations of Generators.- 6.4. Choosing a Good Generator Based on Theoretical Considerations.- 6.4.1. Serial Correlation of Linear Congruential Generato