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Numerical methods for solving discre...

Grassmann, Winfried K.

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Numerical methods for solving discrete event systems = with applications to queueing systems /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Numerical methods for solving discrete event systems/ by Winfried Grassmann, Javad Tavakoli.
其他題名:	with applications to queueing systems /
作者:	Grassmann, Winfried K.
其他作者:	Tavakoli, Javad.
出版者:	Cham :Springer International Publishing : : 2022.,
面頁冊數:	xiv, 362 p. :ill., digital ;24 cm.
內容註:	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.
Contained By:	Springer Nature eBook
標題:	Discrete-time systems - Mathematics. -
電子資源:	https://doi.org/10.1007/978-3-031-10082-6
ISBN:	9783031100826

Numerical methods for solving discrete event systems = with 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. 5..

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

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

3609210
Discrete-time systems
--Mathematics.

LC Class. No.: QA402

Dewey Class. No.: 003.830151

Numerical methods for solving discrete event systems = with applications to queueing systems /
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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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