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.

chapter Chapter 0|7 pages

What this Book Is, and What It Is Not

chapter Chapter 1|20 pages

Large Deviations of Random Variables

chapter Chapter 2|16 pages

General Principles

chapter Chapter 3|7 pages

Random Walks, Branching Processes

chapter Chapter 4|16 pages

Poisson and Related Processes

chapter Chapter 5|60 pages

Large Deviations for Processes

chapter Chapter 6|39 pages

Freidlin-Wentzell Theory

chapter Chapter 7|21 pages

Applications and Extensions

chapter Chapter 8|52 pages

Boundary Theory

part |2 pages


chapter Chapter 9|9 pages

Allocating Independent Subtasks

chapter Chapter 10|5 pages

Parallel Algorithms: Rollback

chapter Chapter 11|27 pages

The M/M/1 Queue

chapter Chapter 12|35 pages

Erlang’s Model

chapter Chapter 13|62 pages

The Anick-Mitra-Sondhi Model

chapter Chapter 14|31 pages


chapter Chapter 15|40 pages

Priority Queues

chapter Chapter 16|12 pages

The Flatto-Hahn-Wright model