The first half is the theory of large deviations developed 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. By developing only what we need for the applications we present, we to keep the theory to a manageable level, both in terms of length and in terms of difficulty. Since our scope is limited to a class of relatively simple processes, the theory is accessible, and less demanding mathematically, than more general treatments. Within our scope, our treatment is detailed, comprehensive and self-contained. As the book shows, there are sufficienty many interesting applications of jump Markov processes to warrant a special treatment. After all, we live in continuous time, and the events that occur in digital equipment are discrete.
We firmly believe that the large deviations of processes should be taught first for jump Markov processes: more difficult processes can be studied once the foundations and the intuition are established. Diffusions are complicated objects, and the student does not need the extra burden of a subtle process to hinder the understanding of large deviations. Discrete time presents another unnecessarily difficult process, because the jumps are usually more general than those of the processes we consider.
The second half of the book is a collection of applications developed at AT&T Bell Laboratories. Our applications cover large areas of the theory of communication networks: circuit-switched transmission (Chapter 12), packet transmission (Chapter 13), multiple access channels (Chapter 14), and the M/M/1 queue (Chapter 11). We cover aspects of parallel computation in a much more spotty fashion: basics of job allocation (Chapter 9), rollback-based parallel simulation (Chapter 10), assorted priority queuing models (Chapter 15) that may be used in performance models of various computer architectures, and asymptotic coupling of processors (Chapter 16).