Large Deviations for Performance Analysis: Queues, Communication and Computing / Edition 1

Large Deviations for Performance Analysis: Queues, Communication and Computing / Edition 1

by Adam Shwartz, Alan Weiss, Shwartz
     
 

This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (iid random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a

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Overview

This book consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (iid random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete-state processes. By developing only what is needed for the applications, the theory is kept to a manageable level, both in terms of length and in terms of difficulty. Within its scope, the treatment is detailed, comprehensive and self-contained. As the book shows, there are sufficiently many interesting applications of jump Markov processes to warrant a special treatment. The second half is a collection of applications developed at Bell Laboratories. The applications cover large areas of the theory of communication networks: circuit-switched transmission, packet transmission, multiple access channels, and the M/M/1 queue. Aspects of parallel computation are covered as well: basics of job allocation, rollback-based parallel simulation, assorted priority queueing models that might be used in performance models of various computer architectures, and asymptotic coupling of processors. These applications are thoroughly analyzed using the tools developed in the first half of the book.
Features: A transient analysis of the M/M/1 queue; a new analysis of an Aloha model using Markov modulated theory; new results for Erlang's model; new results for the AMS model; analysis of "serve the longer queue", "join the shorter queue" and other simple priority queues; and a simple analysis of the Flatto-Hahn-Wright model of processor-sharing.

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Product Details

ISBN-13:
9780412063114
Publisher:
Taylor & Francis
Publication date:
09/01/1995
Series:
Stochastic Modeling Series, #5
Edition description:
1st ed
Pages:
560
Product dimensions:
6.10(w) x 9.10(h) x 1.40(d)
Age Range:
18 Years

Table of Contents

Table of contents
0What this Book Is, and What It Is Not1
1Large Deviations of Random Variables9
2General Principles29
3Random Walks, Branching Processes45
4Poisson and Related Processes53
5Large Deviations for Processes69
6Freidlin-Wentzell Theory129
7Applications and Extensions169
8Boundary Theory191
9Allocating Independent Subtasks245
10Parallel Algorithms: Rollback255
11The M/M/1 Queue261
12Erlang's Model289
13The Anick-Mitra-Sondhi Model325
14Aloha387
15Priority Queues419
16The Flatto-Hahn-Wright model459
AAnalysis and Probability471
BDiscrete-Space Markov Processes499
CCalculus of Variations515
DLarge Deviations Techniques527
References539
Index551

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