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Nelson R. Probability, Stochastic Processes and Queueing Theory. The Mathematics of Computer Performance Modeling

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Nelson R. Probability, Stochastic Processes and Queueing Theory. The Mathematics of Computer Performance Modeling
New York: Springer, 1995. — 590 p. — ISBN 9780387944524, 0387944524.
This textbook provides a comprehensive introduction to probability and stochastic processes, and shows how these subjects may be applied in computer performance modeling. The author's aim is to derive probability theory in a way that highlights the complementary nature of its formal, intuitive, and applicative aspects while illustrating how the theory is applied in a variety of settings. Readers are assumed to be familiar with elementary linear algebra and calculus, including being conversant with limits, 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 combinatorics, 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, matrix geometric techniques, reversibility, and networks of queues. Examples and applications are drawn from problems in computer performance modeling. Throughout, large numbers of exercises of varying degrees of difficulty will help to secure a reader's understanding of these important and fascinating subjects.
Preface
Contents
Figures
Tables
Introduction
Randomness & Probability
Combinatorics
Random Variables & Distributions
Expectation & Fundamental Theorems
Poisson Process & Renewal Theory
M/G/1 Queue
Markov Processes
Matrix Geometric Solutions
Queueing Networks
Epilogue & Special Topics
Types of Randomness
Combinatorial Equalities & Inequalities
Tables of Laplace Transforms & Generating Functions
Limits & Order Relationships
List of Common Summations
Biblio
Refs
Notation
Index
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