This graduate textbook provides an alternative to discrete event simulation. It describes how to formulate discrete event systems, how to convert them into Markov chains, and how to calculate their transient and equilibrium probabilities. The most appropriate methods for finding these probabilities are described in some detail, and templates for efficient algorithms are provided. These algorithms can be executed on any laptop, even in cases where the Markov chain has hundreds of thousands of states. This book features the probabilistic interpretation of Gaussian elimination, a concept that unifies many of the topics covered, such as embedded Markov chains and matrix analytic methods.

The material provided should aid practitioners significantly to solve their problems. This book also provides an interesting approach to teaching courses of stochastic processes.

About the Author

Winfried Grassmann completed his Ph.D. at the University of Zurich, Switzerland, in 1967 with summa cum laude. After four years working as an operations research analyst at Swissair, the Swiss flag carrier, He joined the University of Saskatchewan, Canada, to teach operations research and computer science. Author of three books and numerous articles, Grassmann introduced the randomization method as a numerical tool and invented the Grassmann-Taksar-Heyman (GTH) method.

Javad Tavakoli holds a PhD in Categorical Algebra from Dalhousie University, NS, Canada. In 1996 he proudly had the opportunity to meet with Winfried Grassmann at the University of Saskatchewan, Canada, where he started his new research area in Applied Probability and Stochastic Processes. Javad Tavakoli has been a researcher and educator at the University of British Columbia Okanagan, Canada since 2003. He published a number of papers in Queuing Theory, mostly with Winfried Grassmann. Javad Tavakoli also has received several awards for teaching excellence and published a pre-calculus book from the indigenous perspective.

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