Dayar Analyzing Markov Chains using Kronecker Products

Theory and Applications
1. Auflage 2012
ISBN: 978-1-4614-4190-8
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 86 Seiten

Reihe: Mathematics and Statistics

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.

Zielgruppe

Research

Autoren/Hrsg.

Dayar, Tugrul

Inhaltsverzeichnis

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