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.

Includes eight large case studies to help explain concepts and motivate use of methods in detail Examples provided demonstrate in an easy-to-follow manner the Kronecker structure associated with the transition matrix of the model Provides links to relevant software

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