Control Techniques for Complex Networks
By Sean Meyn, Cambridge, Cambridge University Press, 2007, xvi+pp., £45.00 or US$80.00 (hardback), ISBN 978 0 521 88441 9
Our everyday life is filled with incredibly complex networks, from power lines to the spread of viruses. Such networks are too complex to model accurately, yet too important to have a very simplistic model for. This book aims to provide the reader with a set of tools, as well as methodology, with which to build network models that are able to capture essential dynamics while producing models that are simple enough to create effective controllers.
This book, among others, is being used for a graduate engineering course on the control of stochastic systems. This is appropriate as the book presents a no-nonsense view of complex networks requiring knowledge of stochastic processes from a measure-theoretic viewpoint. The author has included numerous examples and real life motivations for the theory presented. The whole second chapter is devoted to presenting models that are used and referenced throughout the text, allowing for easy reference. Unfortunately this entails a lot of page turning that would perhaps have been simpler using a digital version. By far, I would consider the book's strongest attribute the number of useful topics covered in a succinct way.
Unfortunately the text has a few irritating faults. The number of errors, especially typographical errors, was a surprise. These errors were, however, noncritical and should not hamper understanding. In one instance a typographical error and nonstandard notation combined such that one had to page around to figure out if the formula contains an error or if it is the implicit introduction of a notation. The index is also inadequate and the figures, at times, merely adequate. The author also likes to introduce a lot of notation and one finds formulae like u ε U ⋄ (x − 1 j + 1 j+). This, without a table of symbols, makes the book difficult to use in a nonlinear fashion.
The author has tried to make the book more accessible to advanced undergraduate students by including preliminary theory from mathematics and statistics (quick introductions to linear programming, stochastic processes, random walks, martingales, etc.). Unfortunately this part serves no other purpose than to inform the reader what he/she should know and would need to find out about as one can only review, instead of learn, that knowledge from the given description.
This book is geared towards graduate students and above, with the later chapters intended for researchers. For this audience I think it would provide new ideas and new tools. The concepts explored are so pervasive in our society that I think this book could be used by individuals from numerous fields. I would definitely recommend it to anyone involved with queuing theory.