Queues are everywhere: in computers, in communication and information systems, in production systems, and in service systems (such as call centers). Hence, it is extremely important to be able to design, control, and analyze the performance of queueing systems.

While many introductory books dealing with queues exist, this book is not your usual introduction to queueing theory. You don’t usually find that Little’s Law is presented in chapter 1.

The first chapter deals with basic topics (those that an introduction to queueing theory would discuss in the fourth of fifth chapter) such as stability conditions and Kendall’s notation, in addition to the discussion of Little’s Law.

Chapters 2 and 3 deal with Markovian systems, discussing topics such as finite-state Markov chains and closed-form expressions (for example, how to solve balance equations via cuts or generating functions).

Chapter 4 relaxes the Markovian assumptions and presents the analysis of several queues with general inter-arrival and/or service times, for example, M/G/1, G/M/1, G/G/1, M/G/n, G/M/n, G/G/n and so on.

Chapter 5 discusses multiclass queueing systems under various service disciplines (for example, shortest job first or shortest remaining processing time), while the following two chapters introduce topics related to queueing networks, including open and closed Jackson networks, multiclass networks, and approximations for general queueing networks (for example, decomposition for open networks and mean value analysis for closed networks).

Next, the author discusses fluid models for queueing systems. Chapter 8 starts with an introduction to deterministic fluid queues, covers fluid models for the stability analysis of queueing networks (including multiclass networks), and then discusses diffusion approximations for a number of multiserver queues (including queues with abandonment).

Next, chapter 9 deals with the exact analysis of stochastic fluid queues, while chapter 10 discusses bounds and tail asymptotics.

The book ends with two appendices on random variables (including generating functions and transforms, as well as a discussion of the exponential distribution) and stochastic processes (including discrete and continuous-time Markov chains and Brownian motion).

Overall, the author does a very good job, covering a number of important topics that are not usually found in other books (such as fluid queues and diffusion approximations). Also, it is worth noting that many examples, case studies, problems with related solutions, and paradoxes are used throughout the book. I really liked those regarding the stability of queueing networks, especially in Section 8.2.

However, I had the feeling that, at times, the author tended to overcomplicate relatively simple concepts with an excessive amount of math. Hence, as noted above, this is not the best choice if you are looking for an introduction to queueing theory. If instead you are interested in advanced topics, then this is the book for you.