Analyzing Markov Chains using Kronecker Products

Theory and Applications

  • Tuğrul Dayar

Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Tuğrul Dayar
    Pages 1-7
  3. Tuğrul Dayar
    Pages 9-19
  4. Tuğrul Dayar
    Pages 21-35
  5. Tuğrul Dayar
    Pages 37-56
  6. Tuğrul Dayar
    Pages 57-73
  7. Tuğrul Dayar
    Pages 75-75
  8. Back Matter
    Pages 77-86

About this book

Introduction

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.

Keywords

Kronecker Products Markov Chains Preprocessing Stochastic Processes iterative methods matrix analytic methods

Authors and affiliations

  • Tuğrul Dayar
    • 1
  1. 1., Department of Computer EngineeringBilkent UniversityAnkaraTurkey

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4190-8
  • Copyright Information Tugrul Dayar 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4189-2
  • Online ISBN 978-1-4614-4190-8
  • Series Print ISSN 2191-8198
  • Series Online ISSN 2191-8201
  • About this book