Overview
Part of the book series: International Series in Operations Research & Management Science (ISOR, volume 24)
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Table of contents (12 chapters)
Keywords
About this book
The work of major research scholars in this field comprises the individual chapters of Computational Probability. The first chapter describes, in nonmathematical terms, the challenges in computational probability. Chapter 2 describes the methodologies available for obtaining the transition matrices for Markov chains, with particular emphasis on stochastic Petri-nets. Chapter 3 discusses how to find transient probabilities and transient rewards for these Markov chains. The next two chapters indicate how to find steady-state probabilities for Markov chains with a finite number of states. Both direct and iterative methods are described in Chapter 4. Details of these methods are given in Chapter 5. Chapters 6 and 7 deal with infinite-state Markov chains, which occur frequently in queueing, because there are times one does not want to set a bound for all queues. Chapter 8 deals with transforms, in particular Laplace transforms. The work of Ward Whitt and his collaborators, who have recently developed a number of numerical methods for Laplace transform inversions, is emphasized in this chapter. Finally, if one wants to optimize a system, one way to do the optimization is through Markov decision making, described in Chapter 9. Markov modeling has found applications in many areas, three of which are described in detail:Chapter 10 analyzes discrete-time queues, Chapter 11 describes networks of queues, and Chapter 12 deals with reliability theory.
Editors and Affiliations
Bibliographic Information
Book Title: Computational Probability
Editors: Winfried K. Grassmann
Series Title: International Series in Operations Research & Management Science
DOI: https://doi.org/10.1007/978-1-4757-4828-4
Publisher: Springer New York, NY
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eBook Packages: Springer Book Archive
Copyright Information: Springer Science+Business Media New York 2000
Hardcover ISBN: 978-0-7923-8617-9Published: 31 October 1999
Softcover ISBN: 978-1-4419-5100-7Published: 06 December 2010
eBook ISBN: 978-1-4757-4828-4Published: 14 March 2013
Series ISSN: 0884-8289
Series E-ISSN: 2214-7934
Edition Number: 1
Number of Pages: VIII, 490
Topics: Operations Research/Decision Theory, Probability Theory and Stochastic Processes, Statistics, general