Many practical systems fall under the theoretical framework of uncertain dynamical systems, which are then conveniently modeled according to probabilistic or random models. Simulation of such models constitutes a very important aspect of understanding the underlying physical system behavior. This monograph, Simulation and the Monte Carlo method, presents techniques or methods that are useful in simulating the behavior of many practical systems. Application of such techniques or methods can be found in many diverse areas, including defense, computer communication networks, and manufacturing systems.

Because random models are at the heart of simulating the behavior of practical systems, the book provides a brief review of random variables and random processes and their characterization in chapter 1. Chapter 2 then looks at simulation techniques for some of these random variables and processes using a simple uniform random generator. Indeed, such techniques are the basic building blocks for advanced simulation techniques. Chapter 3 deals with simulation techniques for discrete event systems; many queueing-based systems like computer networks and traffic flow, to name a few, can be accurately modeled using discrete event systems. Chapter 4 deals with the statistical analysis of static and dynamic simulation models. Chapter 5 deals with variance reduction techniques like importance sampling, which are at the heart of many nonlinear filtering problems that occur in many practical systems. Chapter 6 gives an overview of Markov chain Monte Carlo (MCMC) techniques that are used for generating samples from any arbitrary probability distribution, while chapter 7 is devoted to sensitivity analysis of MCMC techniques. Chapter 8 deals with the cross-entropy (CE) method that is mainly used for simulating rare event systems, although the authors also present how the CE method can be modified for combinatorial optimization problems that occur often in graph theory. Chapter 9 presents the splitting method, which can be used “to decompose a ‘difficult’ problem into a sequence of ‘easy’ problems.” The splitting method is central to the simulation, estimation, and optimization of several rare event systems. Finally, chapter 10 presents a new Monte Carlo simulation technique, stochastic enumeration, useful for solving many combinatorial optimization problems.

The third edition of Simulation and the Monte Carlo method significantly enhances the coverage of several topics in chapters 1 to 8. Specifically, the material on random generation has been revised to include multiple recursive generators and the Mersenne Twister. Chapter 5, on variance reduction techniques, has been updated to include a discussion of the multilevel Monte Carlo method. Chapters 9 and 10 are brand new to this edition and have been added to bring in some of the Monte Carlo techniques for solving complex combinatorial optimization problems. In summary, the authors made a systematic effort to update the second edition and come out with a book that is more in sync with the latest developments in MCMC simulation.

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