This fundamental exposition of queueing theory, written by leading researchers, answers the need for a mathematically sound reference work on the subject and has become the standard reference. The thoroughly revised second edition contains a substantial number of exercises and their solutions, which makes the book suitable as a textbook.

This textbook provides a comprehensive introduction to probability and stochastic processes, and shows how these subjects may be applied in computer performance modelling. The author's aim is to derive the theory in a way that combines its formal, intuitive, and applied aspects so that students may apply this indispensable tool in a variety of different settings. Readers are assumed to be familiar with elementary linear algebra and calculus, including the concept of limit, but otherwise this book provides a self-contained approach suitable for graduate or advanced undergraduate students. The first half of the book covers the basic concepts of probability including expectation, random variables, and fundamental theorems. In the second half of the book the reader is introduced to stochastic processes. Subjects covered include renewal processes, queueing theory, Markov processes, and reversibility as it applies to networks of queues. Examples and applications are drawn from problems in computer performance modelling.

Queues and stochastic networks are analyzed in this book with purely probabilistic methods. The purpose of these lectures is to show that general results from Markov processes, martingales or ergodic theory can be used directly to study the corresponding stochastic processes. Recent developments have shown that, instead of having ad-hoc methods, a better understanding of fundamental results on stochastic processes is crucial to study the complex behavior of stochastic networks. In this book, various aspects of these stochastic models are investigated in depth in an elementary way: Existence of equilibrium, characterization of stationary regimes, transient behaviors (rare events, hitting times) and critical regimes, etc. A simple presentation of stationary point processes and Palm measures is given. Scaling methods and functional limit theorems are a major theme of this book. In particular, a complete chapter is devoted to fluid limits of Markov processes.