Examples of queueing abound in daily life: at a ticket window in a railway station or post office, at cash points in the supermarket, and in the waiting room of a hospital. However, it is in telecommunications where queueing theory plays its most important role. The data packets arriving at the input port of a router or switch are buffered in the output queue before transmission to the next hop toward the destination.

Several books have already been dedicated to queueing theory in telecommunications [1,2,3,4]. However, of all the introductory textbooks I know on queueing theory, this is the most accessible.

The book begins with a review of some necessary mathematics. It is assumed that the reader has a prerequisite knowledge of probability theory, transform theory, and matrices. Indeed, the brief refresher on those theories is sufficient to understand most of the mathematical content of the book. Nevertheless, as a novice in queueing modeling, I would have preferred an opening chapter with motivating examples, as in Daigle’s book [1], before starting with theory.

In chapter 2, the reader is introduced to the basic structure, the terminology, and the characteristics of queueing systems. The most commonly used stochastic process for modeling the arrival of customers to a queue is also examined. This chapter is a very gentle introduction to queueing systems.

Each queueing system can be mapped, in principle, to an instance of a Markov process, and then mathematically analyzed. For example, a Markov chain can be used to obtain the probability mass function of the number of customers in a queueing system. Discrete and continuous Markov processes are therefore studied in chapter 3, with a particular focus on the important special case, the so-called birth-death process.

Those Markov processes are then applied to the study of single queues in chapter 4. A Markovian queueing system is one characterized by a Poisson arrival process and exponentially distributed service times. This type of queueing model is the most useful in the study of telephone networks, so dedicating almost 40 pages to it is fully justified.

Packet-switched networks, however, can be better described by semi-Markov processes, presented in chapter 5. Here, the arrival or service process is no longer memoryless, and one cannot set up balance equations for the process. The most frequently used method for solving this problem is the imbedded Markov chain. Another approach is the residual service time method. Both methods are given due attention in chapter 5.

Many realistic applications deploy more than one queue, and most often there is some form of interaction between them. The analysis of networks of queues is much more complicated, though. The state of one queue is generally dependent on the others because of feedback loops. From a topology point of view, queueing networks can be categorized into two generic classes: open and closed. In open queueing networks, customers arrive from external sources, go through several queues, and finally leave the system. Open queueing networks, in particular tandem queues and Jackson queueing networks, are discussed in chapter 6. When customers do not arrive at or depart from the system, the queueing network is called closed. In this case, there is a constant number of customers simply circulating through the various queues. Closed queueing networks, introduced in chapter 7, are often more useful than their open counterparts because the customer population is usually finite. Although queueing networks are mathematically more challenging, the authors manage to keep the pace of an introductory textbook.

Chapter 8 looks at some classes of arrival processes more exotic than Poisson processes, namely Markov-modulated processes. The chapter also very briefly introduces a network calculus that supports the derivation of deterministic bounds. Network calculus analyzes queues from a very different perspective than that of classical queueing theory. The overview of network calculus is new to this edition.

Also with the second edition came a chapter on flow and congestion control. It is somewhat astounding that these control mechanisms are discussed for the somewhat outdated asynchronous transfer mode (ATM) networks instead of Internet protocol (IP) based networks.

The book contains many worked examples illustrating the possible applications of queueing theory. Unfortunately, not all of the examples are drawn from communications networks. Each chapter--except for the last one--concludes with some problem questions.

The book is well written and nicely illustrated. I recommend it as an introduction for graduate students and telecommunications engineers.