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9780898714258 Academic Inspection Copy

Introduction to Matrix Analytic Methods in Stochastic Modeling

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Matrix analysis methods are popular as modelling tools because they give one the ability to construct and analyze a wide class of queuing models in a unified and algorithmically tractable way. The authors present the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date and comprehensive manner. In the current literature, a mixed bag of techniques is used - some probabilistic, some from linear algebra, and some from transform methods. Here, many new proofs that emphasize the unity of matrix analytic approach are included. Applied probabilists, systems analysts, operations research analysts, applied statisticians, and communication and computer engineers as well as electrical engineers interested in modelling and industrial engineers interested in manufacturing systems should find this book useful. Undergraduate advanced calculus and linear algebra and a course in stochastic processes are necessary prerequisites for understanding the book.
Preface Part I: Quasi-Birth-and-Death Processes. Chapter 1: Examples Part II: The Method of Phases. Chapter 2: PH Distributions Chapter 3: Markovian Point Processes Part III: The Matrix-Geometric Distribution. Chapter 4: Birth-and-Death Processes Chapter 5: Processes Under a Taboo Chapter 6: Homogeneous QBDs Chapter 7: Stability Condition Part IV: Algorithms. Chapter 8: Algorithms for the Rate Matrix Chapter 9: Spectral Analysis Chapter 10: Finite QBDs Chapter 11: First Passage Times Part V: Beyond Simple QBDs. Chapter 12: Nonhomogeneous QBDs Chapter 13: Processes, Skip-Free in One Direction Chapter 14: Tree Processes Chapter 15: Product Form Networks Chapter 16: Nondenumerable States Bibliography Index.
Presents the basic mathematical ideas and algorithms of the matrix analytic theory in a readable, up-to-date, and comprehensive manner.
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