Kronecker Modeling and Analysis of Multidimensional Markovian Systems

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.

List of contents

Introduction.- Modeling with Kronecker Products.- Avoiding Unreachable States.- Preprocessing.- Vector-Kronecker Product Multiplication.- Steady-State Analysis.- Transient Analysis.- Conclusion.

Summary

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.

Product details

• Authors: Tu¿rul Dayar, Tugrul Dayar, Tuğrul Dayar
• Publisher: Springer, Berlin
• Languages: English
• Product format: Hardback
• Released: 01.01.2018
• EAN: 9783319971285
• ISBN: 978-3-31-997128-5
• No. of pages: 269
• Dimensions: 157 mm x 245 mm x 23 mm
• Weight: 602 g
• Illustrations: XX, 269 p. 23 illus.
• Series: Springer Series in Operations Research and Financial Engineering; Springer Series in Operations Research and Financial Engineering
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; B, Systemanalyse und -design, Mathematics and Statistics, Probability Theory and Stochastic Processes, Computational Mathematics and Numerical Analysis, Systems analysis & design, Computer mathematics, Numerical analysis, Probabilities, Stochastics, Probability Theory, Computer system failures, System Performance and Evaluation