Kronecker Modeling and Analysis of Multidimensional Markovian Systems

  • Tuğrul Dayar

Table of contents

  1. Front Matter
    Pages i-xx
  2. Tuǧrul Dayar
    Pages 1-11
  3. Tuǧrul Dayar
    Pages 13-46
  4. Tuǧrul Dayar
    Pages 47-103
  5. Tuǧrul Dayar
    Pages 105-157
  6. Tuǧrul Dayar
    Pages 159-178
  7. Tuǧrul Dayar
    Pages 179-227
  8. Tuǧrul Dayar
    Pages 229-244
  9. Tuǧrul Dayar
    Pages 245-247
  10. Back Matter
    Pages 249-269

About this book


This work considers Kronecker-based models with finite as well as countably infinite state spaces for multidimensional Markovian systems by paying particular attention to those whose reachable state spaces are smaller than their product state spaces. Numerical methods for steady-state and transient analysis of Kronecker-based multidimensional Markovian models are discussed in detail together with implementation issues. Case studies are provided to explain concepts and motivate use of methods.

Having grown out of research from the past twenty years, this book expands upon the author’s previously published book Analyzing Markov Chains using Kronecker Products (Springer, 2012). The subject matter is interdisciplinary and at the intersection of applied mathematics and computer science. The book will be of use to researchers and graduate students with an understanding of basic linear algebra, probability, and discrete mathematics.


Multi-dimensional Markovian Modeling Kronecker Operations Steady-state Analysis Transient Analysis Kronecker Product Markov Chain Compact Solution Vector

Authors and affiliations

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

Bibliographic information

  • DOI
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-97128-5
  • Online ISBN 978-3-319-97129-2
  • Series Print ISSN 1431-8598
  • Series Online ISSN 2197-1773
  • Buy this book on publisher's site