Fundamentals of Matrix-Analytic Methods

verfasst von: Qi-Ming He

Verlag: Springer New York

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

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.

Inhaltsverzeichnis

Frontmatter

Chapter 1. From the Exponential Distribution to Phase-Type Distributions

Abstract

This chapter introduces phase-type distributions. Topics covered in this chapter are: (i) the exponential distribution; (ii) definitions of phase-type distributions; (iii) closure properties of phase-type distributions; (iv) PH-representations; (v) multivariate phase-type distributions; and (vi) parameter estimation and fitting of phase-type distributions.

Qi-Ming He

Chapter 2. From the Poisson Process to Markovian Arrival Processes

Abstract

This chapter introduces Markovian arrival processes. Topics covered include: (i) the Poisson process; (ii) definitions of Markovian arrival processes; (iii) performance measures; (iv) batch Markovian arrival processes; and (v) Markovian arrival processes with marked arrivals.

Qi-Ming He

Chapter 3. From the Birth-and-Death Process to Structured Markov Chains

Abstract

This chapter introduces Markov chains of QBD, M/G/1, and GI/M/1 types. Matrix-geometric solutions for the stationary distributions are presented with probabilistic interpretations. Algorithms are developed for computing performance measures. Markov chains of QBD, M/G/1, and GI/M/1 types with a tree structure are also introduced and analyzed. Some results on tail asymptotics of Markov chains with infinitely many background phases are given as well.

Qi-Ming He

Chapter 4. Applications in Queueing Theory

Abstract

This chapter focuses on the applications of the matrix-analytic methods developed in Chaps. 1, 2, and 3 in queueing theory. The emphasis is on both the introduction of analytically and numerically tractable stochastic models and the analysis of such models. The first part of this chapter deals with a number of simple and classical queueing models. The second part analyzes a few queueing models with multiple types of customers. Algorithms for computing performance measures are developed.

Qi-Ming He

Chapter 5. Applications in Inventory and Supply Chain Management

Abstract

This chapter studies a number of inventory and supply chain models. Using matrix-analytic methods, algorithms are developed for computing performance measures such as the expected total cost per unit time. For two inventory models, algorithms are developed for computing the optimal policy.

Qi-Ming He

Titel: Fundamentals of Matrix-Analytic Methods
verfasst von: Qi-Ming He
Verlag: Springer New York
Electronic ISBN: 978-1-4614-7330-5
Print ISBN: 978-1-4614-7329-9
DOI: https://doi.org/10.1007/978-1-4614-7330-5