Analyzing Markov Chains using Kronecker Products : Theory and Applications

Dayar, Tugrul

ISBN 10: 1461441897 / ISBN 13: 9781461441892

Edité par Springer, 2012

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Détails bibliographiques

• Titre: Analyzing Markov Chains using Kronecker Products : Theory and Applications
• Éditeur: Springer
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 1461441897
• ISBN à 13 chiffres: 9781461441892
• Reliure: Couverture souple
• État de l'article: As New

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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.