Numerical Methods for Solving Discrete Event Systems: With Applications to Queue

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Numerical Methods for Solving Discrete Event Systems by Winfried Grassmann, Javad Tavakoli

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 material provided should aid practitioners significantly to solve their problems.

FORMAT
Hardcover LANGUAGE
English CONDITION
Brand New Publisher Description

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

Back Cover

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.

Table of Contents

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.

Review

"This monograph is an exciting addition to the queueing/stochastic processes literature,
written by two highly respected senior researchers. … The writing is precise and clear. Well-known models are used as examples to illustrate the methods presented. … It has a huge number of powerful techniques that are not given sufficient focus elsewhere. This may be one of the best books to introduce graduate students … . This monograph is essential for the bookshelf … of every serious queueing theorist." (Myron Hlynka, Mathematical Reviews, December, 2023)

Feature

Provides many algorithms which may serve as templates Includes detailed discussion of randomization/uniformization method Contains chapter-level summaries and exercises

Details ISBN3031100816 Author Javad Tavakoli Short Title Numerical Methods for Solving Discrete Event Systems Publisher Springer International Publishing AG Series CMS/CAIMS Books in Mathematics Language English Year 2022 ISBN-10 3031100816 ISBN-13 9783031100819 Format Hardcover Subtitle With Applications to Queueing Systems Series Number 5 Imprint Springer International Publishing AG Place of Publication Cham Country of Publication Switzerland Pages 362 UK Release Date 2022-11-05 Publication Date 2022-11-05 DEWEY 003.830151 Edition Description 2022 ed. Edition 2022nd Country of Origin NL Product Class Description Mathematics Alternative 9783031100826 Illustrations 2 Illustrations, color; 2 Illustrations, black and white Audience Educational: Primary & Secondary
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