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This is an introductory level text on stochastic modeling. It is suited for undergraduate or graduate students in actuarial science, business management, computer science, engineering, operations research, public policy, statistics, and mathematics. It employs a large number of examples to teach how to build stochastic models of physical systems, analyze these models to predict their performance, and use the analysis to design and control them. The book provides a self-contained review of the relevant topics in probability theory. The rest of the book is devoted to important classes of stochastic models. In discrete and continuous time Markov models it covers the transient and long term behavior, cost models, and first passage times. Under generalized Markov models, it covers renewal processes, cumulative processes and semi-Markov processes. All the material is illustrated with many examples. There is a separate chapter on queueing models. In the chapter on design the author shows how the techniques developed in the text can be used to optimize the performance of a system. Finally, in the last chapter, linear programming is used to compute optimal control policies for stochastic systems. The book emphasizes numerical answers to the problems. A software package called MAXIM, which runs on MATLAB, is made available for downloading. Vidyadhar G. Kulkarni is Professor of Operations Research at the University of North Craolina at Chapel Hill. He has authored a graduate level text'Modeling and Analysis of Stochastic Systems'and research articles on stochastic models of queues, computer systems and telecommunication systems. He holds a patent on traffic management in telecommunication networks, and he has served as an editor and associate editor of Stochastic Models and Operations Research Letters.

This is an introductory-level text on stochastic modeling. It is suited for undergraduate students in engineering, operations research, statistics, mathematics, actuarial science, business management, computer science, and public policy. It employs a large number of examples to teach the students to use stochastic models of real-life systems to predict their performance, and use this analysis to design better systems. The book is devoted to the study of important classes of stochastic processes: discrete and continuous time Markov processes, Poisson processes, renewal and regenerative processes, semi-Markov processes, queueing models, and diffusion processes. The book systematically studies the short-term and the long-term behavior, cost/reward models, and first passage times. All the material is illustrated with many examples, and case studies. The book provides a concise review of probability in the appendix. The book emphasizes numerical answers to the problems. A collection of MATLAB programs to accompany the this book can be downloaded from http://www.unc.edu/~vkulkarn/Maxim/maxim.zip. A graphical user interface to access the above files can be downloaded from http://www.unc.edu/~vkulkarn/Maxim/maximgui.zip. The second edition incorporates several changes. First its title reflects the changes in content: the chapters on design and control have been removed. The book now contains several case studies that teach the design principles. Two new chapters have been added. The new chapter on Poisson processes gives more attention to this important class of stochastic processes than the first edition did. The new chapter on Brownian motion reflects its increasing importance as an appropriate model for a variety of real-life situations, including finance.

This volume provides an exposition of some fundamental aspects of the asymptotic theory of statistical experiments. The most important of them is “how to construct asymptotically optimal decisions if we know the structure of optimal decisions for the limit experiment”.