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Presents basic techniques in Matrix-Analytic Methods important to stochastic modeling, including conditional probabilities on the phase of Markov chains, the use of nonnegative matrices and M-matrices
Provides a detailed analysis of some queuing, inventory, and supply chain models
Includes examples and exercises
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.
Content Level »Graduate
Keywords »Algorithmic Approach - Applied Probability - Inventory Control - Markov Chains - Matrix-analytic Methods - Nonnegative Matrix - Probability Distribution - Queuing Theory - Reliability Models - Risk/insurance Analysis - Stochastic Models - Supply Chain Management - Telecommunications
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.