Modeling, Analysis, Design and Control of Stochastic Systems (Springer Texts in Statistics) - Hardcover

Kulkarni, Vidyadhur G.

9780387987255: Modeling, Analysis, Design and Control of Stochastic Systems (Springer Texts in Statistics)

Hardcover

ISBN 10: 0387987258 ISBN 13: 9780387987255

Publisher: Springer-Verlag New York Inc., 2000

An introductory level text on stochastic modelling, suited for undergraduates or graduates in actuarial science, business management, computer science, engineering, operations research, public policy, statistics, and mathematics. It employs a large number of examples to show how to build stochastic models of physical systems, analyse 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: In discrete and continuous time Markov models it covers the transient and long term behaviour, cost models, and first passage times; under generalised Markov models, it covers renewal processes, cumulative processes and semi-Markov processes. All the material is illustrated with many examples, and the book emphasises numerical answers to the problems. A software package called MAXIM, which runs on MATLAB, is available for downloading.

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Review:

From the reviews of the second edition:

“The author has added a new chapter on Poisson processes and another one on Brownian motion. The discussion is kept on an elementary level and does not require any knowledge from measure theory or advanced calculus. ... the text is suitable for an undergraduate course on probabilistic modeling for students from physics, engineering, operations research, computer science, business administration or some related field that needs advanced modeling techniques.” (H. M. Mai, Zentralblatt MATH, Vol. 1222, 2011)

“Suitable for undergraduates in Mathematics, Statistics, Operations Research, Computer Science, Business Administration, Public Policy, etc. This is a very clear and readable text on Markov chains, Poisson processes, continuous time Markov chains, renewal processes, and queuing processes. ... The treatment is very clear, intuitive as well as rigorous, without being pedantic, and full of interesting examples and case studies. ... The book should be fun to teach from and learn from.” (Jayanta K. Ghosh, International Statistical Review, Vol. 80 (3), 2012)

Synopsis:

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".

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