Numerical Methods for Solving Discrete Event Systems - Tavakoli, Javad

Résumé :
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.

Biographie:
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.

Sommaire:
Basic Concepts and Definitions.- Systems with Events Generated by Poisson or by Binomial Processes.- Generating the Transition Matrix.- Systems with Events Created by Renewal Processes.- Systems with Events Created by Phase-type Processes.- Computational Complexity and Rounding and Truncation Errors.- Transient Solutions of Markov Chains.- Moving Toward the Statistical Equilibrium.- Equilibrium Solutions of Markov Chains and Related Topics.- Reducing the State Space Through Censoring and Embedding.- Systems with Independent or Almost Independent Components.- Infinite-State Markov Chains and Matrix Analytic Methods.