Includes bibliographical references.

From Exponential Distribution to Phase-Type Distribution -- From Poisson Process to Markovian Arrival Process -- From Birth-and-Death Process to Structured Markov Chain -- Applications in Queueing Theory -- Applications in Inventory and Supply Chain Management.

Fundamentals of Matrix-Analytic Methods targets advanced-level students in mathematics, engineering and computer science. It focuses on the fundamental parts of Matrix-Analytic Methods, Phase-Type Distributions, Markovian arrival processes and Structured Markov chains and matrix geometric solutions. New materials and techniques are presented for the first time in research and engineering design. This book emphasizes stochastic modeling by offering probabilistic interpretation and constructive proofs for Matrix-Analytic Methods. Such an approach is especially useful for engineering analysis and design. Exercises and examples are provided throughout the book --