Analyzing Markov Chains using Kronecker Products: Theory and Applications - Brossura

Dayar, Tugrul

Brossura

ISBN 10: 1461441897 ISBN 13: 9781461441892

Casa editrice: Springer, 2012

Riassunto

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.

Su questo libro

Recensione

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)

Contenuti

Introduction.- Background.- Kronecker representation.- Preprocessing.- Block iterative methods for Kronecker products.- Preconditioned projection methods.- Multilevel methods.- Decompositional methods.- Matrix analytic methods.

Dettagli dell?edizione

• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 1461441897
• ISBN 13: 9781461441892
• Rilegatura: Copertina flessibile
• Numero di pagine: 96
• Contatto del produttore: {language_tag:it_IT,value:"Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com"}