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OverviewThis textbook provides a comprehensive introduction to probability and stochastic processes, and shows how these subjects may be applied in computer performance modelling. The author's aim is to derive the theory in a way that combines its formal, intuitive, and applied aspects so that students may apply this indispensable tool in a variety of different settings. Readers are assumed to be familiar with elementary linear algebra and calculus, including the concept of limit, but otherwise this book provides a self-contained approach suitable for graduate or advanced undergraduate students. The first half of the book covers the basic concepts of probability including expectation, random variables, and fundamental theorems. In the second half of the book the reader is introduced to stochastic processes. Subjects covered include renewal processes, queueing theory, Markov processes, and reversibility as it applies to networks of queues. Examples and applications are drawn from problems in computer performance modelling. Full Product DetailsAuthor: Randolph NelsonPublisher: Springer-Verlag New York Inc. Imprint: Springer-Verlag New York Inc. Edition: Softcover reprint of the original 1st ed. 1995 Dimensions: Width: 17.80cm , Height: 3.10cm , Length: 25.40cm Weight: 2.310kg ISBN: 9781441928467ISBN 10: 1441928464 Pages: 584 Publication Date: 29 October 2010 Audience: Professional and scholarly , Professional & Vocational , Postgraduate, Research & Scholarly Format: Paperback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1 Introduction.- I Probability.- 2 Randomness and Probability.- 3 Combinatorics.- 4 Random Variables and Distributions.- 5 Expectation and Fundamental Theorems.- II Stochastic Processes.- 6 The Poisson Process and Renewal Theory.- 7 The M/G/1 Queue.- 8 Markov Processes.- 9 Matrix Geometric Solutions.- 10 Queueing Networks.- 11 Epilogue and Special Topics.- A Types of Randomness.- A.1 Randomness: Physical Systems.- A.1.1 Intrinsic Probability.- A.2 Randomness: Deterministic Systems.- A.2.1 The Baker’s Transformation.- A.2.2 Dynamical Systems.- A.3 Deterministic Randomness**.- A.3.1 Isomorphism Between Systems.- A.3.2 Random Newtonian Systems.- A.4 Summary of Appendix A.- A.5 Problems for Appendix A.- B Combinatorial Equalities and Inequalities.- B.1 Noninteger Combinatorial Expressions.- B.2 Binomial Formula.- B.3 Stirling’s (de Moivre’s) Formula.- B.4 Bounds on Factorial Expressions.- B.5 Noninteger Factorials**.- C Tables of Laplace Transforms and Generating Functions.- C.0.1 Laplace Transforms.- C.1 Generating Functions.- D Limits and Order Relationships.- D.1 Limits.- D.2 Order Relationships.- E List of Common Summations.- References.- Index of Notation.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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