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＜電子ブック＞
Numerical Methods for Solving Discrete Event Systems : With Applications to Queueing Systems / by Winfried Grassmann, Javad Tavakoli
(CMS/CAIMS Books in Mathematics. ISSN:27306518 ; 5)

版	1st ed. 2022.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2022
本文言語	英語
大きさ	XIV, 362 p. 4 illus., 2 illus. in color : online resource
著者標目	*Grassmann, Winfried author Tavakoli, Javad author SpringerLink (Online service)
件　名	LCSH:Numerical analysis LCSH:Probabilities LCSH:Stochastic processes LCSH:Mathematics FREE:Numerical Analysis FREE:Probability Theory FREE:Stochastic Processes FREE:Mathematics
一般注記	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. HTTP:URL=https://doi.org/10.1007/978-3-031-10082-6

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