Kronecker Modeling and Analysis of Multidimensional Markovian Systems / by Tuğrul Dayar.

Format:

Book

Author/Creator:

Dayar, Tuğrul., Author.

Series:

Springer Series in Operations Research and Financial Engineering, 1431-8598

Language:

English

Subjects (All):

Probabilities.

Computer science--Mathematics.

Computer science.

Computer system failures.

Probability Theory and Stochastic Processes.

Computational Mathematics and Numerical Analysis.

System Performance and Evaluation.

Local Subjects:

Probability Theory and Stochastic Processes.

Computational Mathematics and Numerical Analysis.

System Performance and Evaluation.

Physical Description:

1 online resource (284 pages).

Edition:

1st ed. 2018.

Place of Publication:

Cham : Springer International Publishing : Imprint: Springer, 2018.

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.

Contents:

Introduction

Modeling with Kronecker Products

Avoiding Unreachable States

Preprocessing

Vector-Kronecker Product Multiplication

Steady-State Analysis

Transient Analysis

Conclusion.

ISBN:

3-319-97129-8