Introduction to Matrix Analytic Methods in Queues 1 Analytical and Simulation Approach - Basics

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.

The book’s detailed approach will make it more accessible for readers interested in learning about MAM in stochastic models.

Srinivas R. Chakravarthy retired from Kettering University in Michigan, USA after serving as Professor of Mathematics, and as Professor and Head of Industrial and Manufacturing Engineering. He was bestowed the Distinguished Faculty (Kettering’s Faculty and Alumni Honor Wall) award in 2015. He obtained his PhD under the supervision of Professor Marcel Neuts and is the co-founder of the International Conference Series on MAM in Stochastic Models. His research interests are in queues, inventory and reliability.

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.