Large deviations for performance analysis. Queues, communications, and computing. With an appendix by Robert J. Vanderbei.

*(English)*Zbl 0871.60021
London: Chapman & Hall. viii, 556 p. (1995).

This book is a successful attempt to apply a sophisticated new mathematical technique, the theory of large deviations, to a broad class of problems in performance analysis of large systems. The theory of large deviations deals with the analysis of small probabilities in the context of various limit theorems. The theory describes the asymptotical convergence rates in terms of variational problems. The aim of this book is to make this theory accessible to engineers and applied-mathematicians for the analysis of several non-trivial problems of the theory of large size communication networks and parallel computations.

The book is divided into two parts. The first part, theoretical, presents a comprehensive introduction to the theory of large deviations. The second part deals with various new applications. In the first part, the authors have focused on the theory for jump Markov process, including complete proofs and new results for the flat boundary case. The second part demonstrates how these results can be applied to various problems, such as circuit-switched and packet transmission, multiple-access channels, M/M/1 queues, rollback-based simulations and assorted priority queueing models. An appendix contains the basic mathematical background from analysis and probability theory. The book requires knowledge in probability and analysis at the level of advanced undergraduate or graduate students.

The book is divided into two parts. The first part, theoretical, presents a comprehensive introduction to the theory of large deviations. The second part deals with various new applications. In the first part, the authors have focused on the theory for jump Markov process, including complete proofs and new results for the flat boundary case. The second part demonstrates how these results can be applied to various problems, such as circuit-switched and packet transmission, multiple-access channels, M/M/1 queues, rollback-based simulations and assorted priority queueing models. An appendix contains the basic mathematical background from analysis and probability theory. The book requires knowledge in probability and analysis at the level of advanced undergraduate or graduate students.

Reviewer: J.D.Deuschel (Berlin)