 Название: Introduction to Matrix Analytic Methods in Queues 1: Analytical and Simulation Approach - Basics
Автор: Srinivas R. Chakravarthy
Издательство: Wiley-ISTE
Год: 2022
Страниц: 370
Язык: английский
Формат: pdf (true), epub (true)
Размер: 18.7 MB
Matrix-analytic methods (MAM) were introduced by Professor Marcel Neuts and have been applied to a variety of stochastic models since. In order to provide a clear and deep understanding of MAM while showing their power, this book presents MAM concepts and explains the results using a number of worked-out examples.
This book’s approach will inform and kindle the interest of researchers attracted to this fertile field. To allow readers to practice and gain experience in the algorithmic and computational procedures of MAM, Introduction to Matrix Analytic Methods in Queues 1 provides a number of computational exercises. It also incorporates simulation as another tool for studying complex stochastic models, especially when the state space of the underlying stochastic models under analytic study grows exponentially.
All the texts mentioned above provide an excellent foundation of a variety of stochastic models in general and of theoretical properties and applications of MAM to those models. The present work takes a different approach by covering the basics of MAM but focusing on clearly illustrating its use in analyzing many stochastic models. It is also my strong belief that the art of model building and analysis is better learned by studying carefully constructed examples and by practicing those skills on other models. A text that incorporates the mathematical ideas of MAM along with clearly illustrated examples on the use of these methods in analyzing interesting stochastic models makes MAM more accessible to current researchers. I believe this juxtaposition reinforces the power of MAM, enables one to appreciate and get better in the art of model building, and helps in improving “probabilistic thinking” of models and solutions. It is also for these reasons that I have included a large collection of exercises, most of which are computational in nature, for the reader to practice, experiment and get the experience in the algorithmic and computational procedures.
The book’s detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.
Contents:
Preface
1 Introduction
2 Markov Chains
3 Discrete Phase Type Distributions
4 Continuous Phase Type Distributions
5 Discrete-Batch Markovian Arrival Process
6 Continuous-Batch Markovian Arrival Process
7 Matrix-Analytic Methods (Discrete-Time)
8 Matrix-Analytic Methods (Continuous-time)
9 Applications
References
Index
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Introduction to Matrix Analytic Methods in Queues 1: Analytical and Simulation Approach - Basics 
