Mathematical methods based on the theory of stochastic processes have long been used effectively in telephone traffic modeling. Today’s packet- or cell-based traffic in broadband communications systems is distinctly different from traditional voice traffic, and generates challenging mathematical and statistical problems. This book provides a concise overview of stochastic models and mathematical techniques for solving some of these problems.

The book begins with a brief introduction to networking concepts and broadband traffic characteristics. Three examples are used to introduce basic techniques from probability theory. Chapter 2 presents Markov systems in discrete and continuous time. Markov birth-and-death processes form the historical core of the subject of traffic modeling, and more general models often presuppose a fair understanding of this class.

Chapter 3 begins with performance measures, and studies load-versus-throughput relationships. Techniques based on renewal theory, and techniques related to general service-time distributions in queuing and loss systems, are introduced. The main focus of this chapter is on non-Markov dynamics.

Chapter 4 is devoted to the simplest loss and contention protocols in packet switching. The basic example is an m * n crossbar switch, where packets arriving on m input lines are randomly switched onto n outputs. This results in either loss or buffer delay, due to contention for output lines. Head-of-line blocking is discussed as well.

Chapter 5 addresses traffic modeling relevant for cell and burst time scales, where chapters 2 and 3 are applied to the cell level. The author presents a model for the multiplexing of independent sources over a joint transmission channel. An important finding from recent research in this area shows that the addition of distributions with heavy tails results in long-range dependence.

In Chapter 6, a number of techniques and models are applied to the study of traffic control. Topics such as effective bandwidth and statistical multiplexing gain are related to admission control. Access control includes several versions of the leaky bucket mechanism. Finally, Internet congestion control with the transmission control protocol’s (TCP) window scheme is studied in detail.

This book is intended for students in mathematics, stochastics, or computer science, and for final-year undergraduates to Ph.Ds. At the end of each chapter, a list of exercises is given, however no solutions are provided. The book is short, but very dense; the author’s clear presentation, based on sound mathematical reasoning, helps readers to understand the well-selected topics better. The book is not easy, but neither is the subject matter.