Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling / Edition 1

Probability, Stochastic Processes, and Queueing Theory: The Mathematics of Computer Performance Modeling / Edition 1

by Randolph Nelson
     
 

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ISBN-10: 1441928464

ISBN-13: 9781441928467

Pub. Date: 10/29/2010

Publisher: Springer New York

This textbook provides a comprehensive introduction to probability and shastic 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.

Overview

This textbook provides a comprehensive introduction to probability and shastic 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 shastic 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.

Product Details

ISBN-13:
9781441928467
Publisher:
Springer New York
Publication date:
10/29/2010
Edition description:
Softcover reprint of hardcover 1st ed. 1995
Pages:
584
Product dimensions:
10.00(w) x 7.00(h) x 1.24(d)

Table of Contents

1 Introduction.- I Probability.- 2 Randomness and Probability.- 3 Combinatorics.- 4 Random Variables and Distributions.- 5 Expectation and Fundamental Theorems.- II Shastic 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.

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