Reversibility and stochastic networks, by Frank P. Kelly, Cambridge, Cambridge University Press, 2011, viii + 230 pp., £30.00 or US$49.00 (paperback), ISBN 978-1-107-40115-0
In this book, the concept of reversibility together with several versions of stochastic networks are explored. Kelly is one of the leading researchers when it comes to model formulation to study stochastic networks and queueing theory. He has authored a large number of important works related to the area and therefore has a deep knowledge of the subject.
The focus of the book is on networks whose mathematical formulation satisfy the reversibility property. However, some cases where the reversibility property is not present are also given. Many examples of the possible applications of the main theme of the book are also given. That is very useful, since the reader may have an idea of how to use the theoretical formulation in real-life problems. The author presents several types of problems that can be studied by making use of stochastic networks and queueing theory. Among them we have migration processes (closed and open) which can be very useful in the study of population genetics, and queueing networks with the presence of a series of queues, which can be very useful in studies related to telephone lines usage, timesharing computing, production lines and road traffic. The subject of clustering processes is also explored as well as its application and a generalisation. Some of their applications and a generalisation of them are also given. Towards the end of the book some spatial processes are also considered.
The book is written in a clear form and the subject is explained in a way that it makes it easier for the reader to follow. However, readers from areas other than mathematics may encounter some difficulties due to the specialised terminology. Hence, it would be advisable for those readers to team up with researchers in the area of probability theory and applications. Researchers in applied mathematics, probability or statistics may find the book a good source of basic models, and not so basic ones, that can be used in a variety of real-world problems. In terms of real applications, some work is left to the reader, since the author only presents the theoretical aspects of the models including the mathematical and probabilistic analysis, but leaves out, for instance, the estimation of the parameters that might be involved in those models.
The list of references is very complete and the way it is also presented, divided by chapter, is very useful. The subject index is complete enough and the inclusion of a symbol index is an extra positive point of the book. The author also presents a list of problems left to the reader to solve. That is very useful and makes the book also suitable to a basic course on the subject. Students would greatly profit from a course whose main reference book is this one.\vfill
Due to its importance, I definitely would recommend the book to be acquired by any library dedicated to mathematics in general. It can be of use to readers with either an interest only in the theoretical aspect of the subject presented or a more applied focus.