Front Cover -- Title Page -- Copyright page -- Table of Contents -- Preface -- Overview -- New to This Edition -- Chapter Descriptions -- Thanks -- 1. Introduction -- Exercises -- 2. Elements of Probability -- 2.1 Sample Space and Events -- 2.2 Axioms of Probability -- 2.3 Conditional Probability and Independence -- 2.4 Random Variables -- 2.5 Expectation -- 2.6 Variance -- 2.7 Chebyshev's Inequality and the Laws of Large Numbers -- 2.8 Some Discrete Random Variables -- Binomial Random Variables -- Poisson Random Variables -- Geometric Random Variables -- The Negative Binomial Random Variable -- Hypergeometric Random Variables -- 2.9 Continuous Random Variables -- Uniformly Distributed Random Variables -- Normal Random Variables -- Exponential Random Variables -- The Poisson Process and Gamma Random Variables -- The Nonhomogeneous Poisson Process -- 2.10 Conditional Expectation and Conditional Variance -- The Conditional Variance Formula -- Exercises -- References -- 3. Random Numbers -- Introduction -- 3.1 Pseudorandom Number Generation -- 3.2 Using Random Numbers to Evaluate Integrals -- Exercises -- References -- 4. Generating Discrete Random Variables -- 4.1 The Inverse Transform Method -- 4.2 Generating a Poisson Random Variable -- 4.3 Generating Binomial Random Variables -- 4.4 The Acceptance-Rejection Technique -- 4.5 The Composition Approach -- 4.6 Generating Random Vectors -- Exercises -- 5. Generating Continuous Random Variables -- Introduction -- 5.1 The Inverse Transform Algorithm -- 5.2 The Rejection Method -- 5.3 The Polar Method for Generating Normal Random Variables -- 5.4 Generating a Poisson Process -- 5.5 Generating a Nonhomogeneous Poisson Process -- Exercises -- References -- 6. The Discrete Event Simulation Approach -- Introduction -- 6.1 Simulation via Discrete Events.

6.2 A Single-Server Queueing System -- 6.3 A Queueing System with Two Servers in Series -- 6.4 A Queueing System with Two Parallel Servers -- 6.5 An Inventory Model -- 6.6 An Insurance Risk Model -- 6.7 A Repair Problem -- 6.8 Exercising a Stock Option -- 6.9 Verification of the Simulation Model -- Exercises -- References -- 7. Statistical Analysis of Simulated Data -- Introduction -- 7.1 The Sample Mean and Sample Variance -- 7.2 Interval Estimates of a Population Mean -- 7.3 The Bootstrapping Technique for Estimating Mean Square Errors -- Exercises -- References -- 8. Variance Reduction Techniques -- Introduction -- 8.1 The Use of Antithetic Variables -- 8.2 The Use of Control Variates -- 8.3 Variance Reduction by Conditioning -- Estimating the Expected Number of Renewals by Time t -- 8.4 Stratified Sampling -- 8.5 Applications of Stratified Sampling -- Analyzing Systems Having Poisson Arrivals -- Computing Multidimensional Integrals of Monotone Functions -- Compound Random Vectors -- 8.6 Importance Sampling -- 8.7 Using Common Random Numbers -- 8.8 Evaluating an Exotic Option -- 8.9 Estimating Functions of Random Permutations and Random Subsets -- Random Permutations -- Random Subsets -- 8.10 Appendix: Verification of Antithetic Variable Approach When Estimating the Expected Value of Monotone Functions -- Exercises -- References -- 9. Statistical Validation Techniques -- Introduction -- 9.1 Goodness of Fit Tests -- The Chi-Square Goodness of Fit Test for Discrete Data -- The Kolmogorov-Smirnov Test for Continuous Data -- 9.2 Goodness of Fit Tests When Some Parameters Are Unspecified -- The Discrete Data Case -- The Continuous Data Case -- 9.3 The Two-Sample Problem -- 9.4 Validating the Assumption of a Nonhomogeneous Poisson Process -- Exercises -- References -- 10. Markov Chain Monte Carlo Methods -- Introduction.

10.1 Markov Chains -- 10.2 The Hastings-Metropolis Algorithm -- 10.3 The Gibbs Sampler -- 10.4 Simulated Annealing -- 10.5 The Sampling Importance Resampling Algorithm -- Exercises -- References -- 11. Some Additional Topics -- Introduction -- 11.1 The Alias Method for Generating Discrete Random Variables -- 11.2 Simulating a Two-Dimensional Poisson Process -- 11.3 Simulation Applications of an Identity for Sums of Bernoulli Random Variables -- 11.4 Estimating the Distribution and the Mean of the First Passage Time of a Markov Chain -- 11.5 Coupling from the Past -- Exercises -- References -- Index.