[PDF] Large Deviations For Performance Analysis eBook

Author : Alan Weiss
Publisher : Routledge
Page : 565 pages
File Size : 25,51 MB
Release : 2019-03-07
Category : Computers
ISBN : 0429846878

GET BOOK

Originally published in 1995, Large Deviations for Performance Analysis consists of two synergistic parts. The first half develops the theory of large deviations from the beginning, 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 including, 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 analysed using the tools developed in the first half of the book.

Author : Michel Mandjes
Publisher : John Wiley & Sons
Page : 336 pages
File Size : 43,78 MB
Release : 2007-04-30
Category : Mathematics
ISBN : 9780470515082

GET BOOK

In recent years the significance of Gaussian processes to communication networks has grown considerably. The inherent flexibility of the Gaussian traffic model enables the analysis, in a single mathematical framework, of systems with both long-range and short-range dependent input streams. Large Deviations for Gaussian Queues demonstrates how the Gaussian traffic model arises naturally, and how the analysis of the corresponding queuing model can be performed. The text provides a general introduction to Gaussian queues, and surveys recent research into the modelling of communications networks. Coverage includes: Discussion of the theoretical concepts and practical aspects related to Gaussian traffic models. Analysis of recent research asymptotic results for Gaussian queues, both in the large-buffer and many-sources regime. An emphasis on rare-event analysis, relying on a variety of asymptotic techniques. Examination of single-node FIFO queuing systems, as well as queues operating under more complex scheduling disciplines, and queuing networks. A set of illustrative examples that directly relate to important practical problems in communication networking. A large collection of instructive exercises and accompanying solutions. Large Deviations for Gaussian Queues assumes minimal prior knowledge. It is ideally suited for postgraduate students in applied probability, operations research, computer science and electrical engineering. The book’s self-contained style makes it perfect for practitioners in the communications networking industry and for researchers in related areas.

Author : Frank Hollander
Publisher : American Mathematical Soc.
Page : 164 pages
File Size : 37,92 MB
Release : 2000
Category : Mathematics
ISBN : 9780821844359

GET BOOK

Offers an introduction to large deviations. This book is divided into two parts: theory and applications. It presents basic large deviation theorems for i i d sequences, Markov sequences, and sequences with moderate dependence. It also includes an outline of general definitions and theorems.

Author : David R. McDonald
Publisher : American Mathematical Soc.
Page : 210 pages
File Size : 35,11 MB
Release : 2000
Category : Mathematics
ISBN : 0821819917

GET BOOK

This volume consists of the proceedings of the Workshop on Analysis and Simulation of Communication Networks held at The Fields Institute (Toronto). The workshop was divided into two main themes, entitled "Stability and Load Balancing of a Network of Call Centres" and "Traffic and Performance". The call centre industry is large and fast-growing. In order to provide top-notch customer service, it needs good mathematical models. The first part of the volume focuses on probabilistic issues involved in optimizing the performance of a call centre. While this was the motivating application, many of the papers are also applicable to more general distributed queueing networks. The second part of the volume discusses the characterization of traffic streams and how to estimate their impact on the performance of a queueing system. The performance of queues under worst-case traffic flows or flows with long bursts is treated. These studies are motivated by questions about buffer dimensioning and call admission control in ATM or IP networks. This volume will serve researchers as a comprehensive, state-of-the-art reference source on developments in this rapidly expanding field.

Author : Amir Dembo
Publisher : Springer Science & Business Media
Page : 409 pages
File Size : 48,8 MB
Release : 2009-11-03
Category : Science
ISBN : 3642033113

GET BOOK

Large deviation estimates have proved to be the crucial tool required to handle many questions in statistics, engineering, statistial mechanics, and applied probability. Amir Dembo and Ofer Zeitouni, two of the leading researchers in the field, provide an introduction to the theory of large deviations and applications at a level suitable for graduate students. The mathematics is rigorous and the applications come from a wide range of areas, including electrical engineering and DNA sequences. The second edition, printed in 1998, included new material on concentration inequalities and the metric and weak convergence approaches to large deviations. General statements and applications were sharpened, new exercises added, and the bibliography updated. The present soft cover edition is a corrected printing of the 1998 edition.

Author : Po-Ning Chen
Publisher : LAP Lambert Academic Publishing
Page : 132 pages
File Size : 42,19 MB
Release : 2010-10
Category :
ISBN : 9783843369992

GET BOOK

This book studies the performance of distributed detection systems by means of large deviation techniques under two distinct models. In the first model, the error performance is investigated as the number of sensors tends to infinity by assuming that the i.i.d. sensor data are quantized locally into m-ary messages and transmitted to the fusion center for binary hypothesis testing. It is found that when the second moment of the post-quantization log-likelihood ratio is unbounded, the Neyman-Pearson error exponent becomes a function of the test level; whereas the Bayes error exponent remains unaffected. Also shown is that in Bayes testing, the equivalence of absolutely optimal and best identical-quantizer systems is not limited to error exponents but extends to the actual Bayes errors up to a multiplicative constant. In the second model, the null and alternative distributions become spatially correlated Gaussian, differing in the mean. The issue considered includes whether contiguous marginal likelihood ratio quantizers are optimal. It is shown that this is not true in general, and a sufficient condition is obtained under the case of a single observation per sensor.

Author : S. R. S. Varadhan
Publisher : American Mathematical Soc.
Page : 114 pages
File Size : 29,24 MB
Release : 2016-12-08
Category : Mathematics
ISBN : 082184086X

GET BOOK

The theory of large deviations deals with rates at which probabilities of certain events decay as a natural parameter in the problem varies. This book, which is based on a graduate course on large deviations at the Courant Institute, focuses on three concrete sets of examples: (i) diffusions with small noise and the exit problem, (ii) large time behavior of Markov processes and their connection to the Feynman-Kac formula and the related large deviation behavior of the number of distinct sites visited by a random walk, and (iii) interacting particle systems, their scaling limits, and large deviations from their expected limits. For the most part the examples are worked out in detail, and in the process the subject of large deviations is developed. The book will give the reader a flavor of how large deviation theory can help in problems that are not posed directly in terms of large deviations. The reader is assumed to have some familiarity with probability, Markov processes, and interacting particle systems.