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Analyzing Markov Chains using Kronecker Products: Theory and Applications (SpringerBriefs in Mathematics) - Softcover
Synopsis
Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.
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Product Description
Analyzing Markov Chains Using Kronecker Products Kronecker products are used to define the underlying Markov chain (MC) invarious modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. This title provides the developments in the solution of such MCs are reviewed from an algebraic point of view.
Review
From the reviews:
“Dayar’s book on Kronecker products for Markov processes addresses an important topic which, up to now, has not been thoroughly discussed as a single entity in the literature. ... The book has numerous examples throughout to illustrate the results and methods which the author presents. ... the book is a valuable tool for learning to apply Kronecker representation to continuous time Markov chains.” (Myron Hlynka, Mathematical Reviews, May, 2013)"About this title" may belong to another edition of this title.
- PublisherSpringer
- Publication date2012
- ISBN 10 1461441897
- ISBN 13 9781461441892
- BindingPaperback
- LanguageEnglish
- Number of pages95
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Taschenbuch. Condition: Neu. Neuware -Kronecker products are used to define the underlying Markov chain (MC) in various modeling formalisms, including compositional Markovian models, hierarchical Markovian models, and stochastic process algebras. The motivation behind using a Kronecker structured representation rather than a flat one is to alleviate the storage requirements associated with the MC. With this approach, systems that are an order of magnitude larger can be analyzed on the same platform. The developments in the solution of such MCs are reviewed from an algebraic point of view and possible areas for further research are indicated with an emphasis on preprocessing using reordering, grouping, and lumping and numerical analysis using block iterative, preconditioned projection, multilevel, decompositional, and matrix analytic methods. Case studies from closed queueing networks and stochastic chemical kinetics are provided to motivate decompositional and matrix analytic methods, respectively.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 96 pp. Englisch. Seller Inventory # 9781461441892
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