Network calculus is defined as:

a set of recent developments that provide deep insights into flow problems encountered in networking. With network calculus, we are able to understand some fundamental properties of integrated services networks, window flow control, scheduling and buffer or delay dimensioning. [1]

Its essential idea is to use alternate algebras, particularly the min-plus algebra and max-plus algebra, to transform complex nonlinear network systems into analytically tractable linear systems.

Excellent books summarizing results for deterministic network calculus are available [2,3]. However, service guarantees are required by multimedia flows in the network, which often tolerate some amount of loss or delay. For such flows, the provision of stochastic service guarantees is more important because they can make better use of the multiplexing gain in the network. As a first step in this direction, this book presents an overall picture of the state of the art of stochastic service guarantee analysis and a comprehensive treatment of this active research area.

The book can be divided into two parts. The first part, consisting of chapters 1 to 6, provides the main set of results; the second part, chapters 7 to 9, presents applications of stochastic network calculus. An appendix discusses open research challenges, for further study of the topic. Chapter 1 gives the basic properties required from a theory of tractable performance analysis of computer networks. Chapter 2 discusses deterministic network calculus. Chapter 3 introduces various stochastic traffic models and their relationships with each other. Chapter 4 defines stochastic server models, and chapter 5 summarizes the basic properties of stochastic network calculus under different combinations of traffic and server models. Chapter 6 focuses on independent case analysis. Chapter 7 analyzes stochastic service guarantees under different scheduling disciplines; this chapter also presents applications to admission control and traffic conformance study. Chapter 8 studies the extent to which a flow becomes nonconformant, with respect to its initial traffic characterization after it passes through a network. Chapter 9 presents an application to generalized processor sharing systems with long-range dependent traffic inputs.

Since many networks, including wireless networks, provide only stochastic service guarantees, and multimedia applications perform well with stochastic guarantees, the results in this book will be useful for analysis and provision of service guarantees in such network scenarios. Skillfully organized, this book covers all essential topics. One of its big successes is its balance between mathematical rigor and practical discussions and guidelines.

The book includes end-of-chapter problems, as well as summaries and bibliographic comments. Overall, the book is easy to read, making it appropriate for an undergraduate or graduate course on the subject. Researchers in the areas of performance evaluation of computer networks and provision and analysis of service guarantees in computer networks will benefit from the comprehensive discussion of stochastic service guarantee issues.