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

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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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Editorial Reviews

Booknews
A text that consists of two synergistic parts. The first half develops the theory of large deviations from the beginning (i.i.d. random variables) through recent results on the theory for processes with boundaries, keeping to a very narrow path: continuous-time, discrete- state processes. The second half is a collection of applications developed at AT&T Bell Laboratories which 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. These applications are analyzed using the tools developed in the first half of the text. Includes an errata sheet. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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Product Details

  • ISBN-13: 9780412063114
  • Publisher: Taylor & Francis
  • Publication date: 9/1/1995
  • Series: Stochastic Modeling Series , #5
  • Edition description: 1st ed
  • Edition number: 1
  • Pages: 560
  • Product dimensions: 6.10 (w) x 9.10 (h) x 1.40 (d)

Table of Contents

Table of contents
0 What this Book Is, and What It Is Not 1
1 Large Deviations of Random Variables 9
2 General Principles 29
3 Random Walks, Branching Processes 45
4 Poisson and Related Processes 53
5 Large Deviations for Processes 69
6 Freidlin-Wentzell Theory 129
7 Applications and Extensions 169
8 Boundary Theory 191
9 Allocating Independent Subtasks 245
10 Parallel Algorithms: Rollback 255
11 The M/M/1 Queue 261
12 Erlang's Model 289
13 The Anick-Mitra-Sondhi Model 325
14 Aloha 387
15 Priority Queues 419
16 The Flatto-Hahn-Wright model 459
A Analysis and Probability 471
B Discrete-Space Markov Processes 499
C Calculus of Variations 515
D Large Deviations Techniques 527
References 539
Index 551
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