We can apply queueing models to any type of service system where items have to wait in queues for service while the server is busy attending to other items. Queueing systems are prevalent in many areas, ranging from transportation to computers, telecommunications, and manufacturing.

Several introductory texts on queueing models exist. However, they either oversimplify the subject matter and its analysis, presenting merely recipes without providing the theoretical background that would enable the reader to adapt the models to their needs, or, more often, they present the theoretical background with such mathematical rigor that practitioners may have difficulty understanding it. (There are two notable recent exceptions to this rule [1,2].) The author manages to bridge the gap between these two approaches by limiting the subject matter to single-node queues in discrete time. This is a reasonable limitation, because most practical queueing problems can be reduced to single-node systems, with the huge advantage that single-node systems in discrete time can be set up as Markov chains, and we can apply the results from the rich literature on Markov chains.

Chapter 1 introduces single-node queueing systems, and makes a quick comparison between discrete and continuous time analyses. Chapter 2 begins by briefly reviewing stochastic processes as an introduction to the Markov process. Markov processes are stochastic processes where the state of the system in the future is independent of the past history, but only dependent on the present. Markov processes are usually modeled as Markov chains. In this chapter, the emphasis is on computational approaches for analyzing certain important classes of Markov chains, such as bivariate discrete-time and infinite-state Markov chains.

In chapter 3, the author analyzes in more detail two basic processes that define a single-node queueing system: the arrival process and the service process. Most books discuss these two processes separately, but here the author combines them, since the probability distributions used for service processes can also be used for the inter-arrival times.

Most introductory books also start with the Poisson process, because it is the easiest one to analyze. This book, however, does not even mention Poisson processes. Instead, it uses the much less-known but easily accessible phase-type distribution.

Chapter 4 discusses approximately ten queueing models in more detail, using the well-known Kendall notation. As promised by the author, the book uniformly presents all models as transition matrices of the corresponding Markov chains, making the different models very comparable.

The last chapter presents more advanced single-node queueing models: multi-server queues, priority queues, vacation queues, and queues with multiple classes of packets. I have rarely seen the latter two addressed in textbooks.

The book has some minor flaws. The index lists only about 60 entries. Entries on Kendall’s notation; first in, first out (FIFO); first-come, first-served (FCFS); and many others are missing. A list of abbreviations is also sadly absent.

Although I find the strict limitation to single-node queues very appealing, I would not recommend this book as a first introduction to queueing theory. Here, I prefer the more classical approach of other texts [1,2]. The book makes a good supplement to the classical approach, however, presenting the subject matter in a refreshing way.