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Numerical methods for solving discrete event systemswith applications to queueing systems /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Numerical methods for solving discrete event systemsby Winfried Grassmann, Javad Tavakoli.
Reminder of title:	with applications to queueing systems /
Author:	Grassmann, Winfried K.
other author:	Tavakoli, Javad.
Published:	Cham :Springer International Publishing :2022.
Description:	xiv, 362 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Discrete-time systemsMathematics.
Online resource:	https://doi.org/10.1007/978-3-031-10082-6
ISBN:	9783031100826$q(electronic bk.)

Numerical methods for solving discrete event systemswith applications to queueing systems /
Grassmann, Winfried K.

Numerical methods for solving discrete event systemswith applications to queueing systems /[electronic resource] :by Winfried Grassmann, Javad Tavakoli. - Cham :Springer International Publishing :2022. - xiv, 362 p. :ill., digital ;24 cm. - CMS/CAIMS books in mathematics,v. 52730-6518 ;. - CMS/CAIMS books in mathematics ;v. 3..

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.

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.

ISBN: 9783031100826$q(electronic bk.)

Standard No.: 10.1007/978-3-031-10082-6doiSubjects--Topical Terms:

939434
Discrete-time systems
--Mathematics.

LC Class. No.: QA402

Dewey Class. No.: 003.830151

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505 0 $a 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.
520 $a 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.
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