Reversibility and Stochastic Networks: (Cambridge Mathematical Library)

This classic in stochastic network modelling broke new ground when it was published in 1979, and it remains a superb introduction to reversibility and its applications. The book concerns behaviour in equilibrium of vector stochastic processes or stochastic networks. When a stochastic network is reversible its analysis is greatly simplified, and the first chapter is devoted to a discussion of the concept of reversibility. The rest of the book focuses on the various applications of reversibility and the extent to which the assumption of reversibility can be relaxed without destroying the associated tractability. Now back in print for a new generation, this book makes enjoyable reading for anyone interested in stochastic processes thanks to the author's clear and easy-to-read style. Elementary probability is the only prerequisite and exercises are interspersed throughout.

Table of Contents:
1. Markov processes and reversibility; 2. Migration processes; 3. Queueing networks; 4. Examples of queueing networks; 5. Electrical analogues; 6. Reversible migration processes; 7. Population genetics models; 8. Clustering processes; 9. Spatial processes; References; Symbol index; Subject index.

About the Author :
F. P. Kelly is Professor of the Mathematics of Systems in the Statistical Laboratory, University of Cambridge.

Review :
'… the exposition is clear and precise without being pedantic … essential (and enjoyable) reading for any operational researcher. But not only for him, because as so often with good mathematics, these methods draw together many diverse applied fields.' J. F. C. Kingman, European Journal of Operational Research 'Its wealth of ideas is so rich and (as in much of Kelly's work) it starts with very elementary ideas which in his hands are built up until suddenly you have something that is very valuable … It is a book that should be on the shelf of anyone working on stochastic networks.' Onna Boxma, EURANDOM and Eindhoven University of Technology 'This superb book displays the power and beauty of combining two simple ideas … Kelly progresses in easy, intelligible steps through an enormous range of models. He weaves general theorems together with concrete applications that lead to explicit formulas … Kelly illuminates his material with the understanding and care of an old jeweller examining a diamond … Topics once presented reappear as new theorems and throughout the book are comments that convey, and reveal on the part of the author, a wonderful insight into how all parts of the book are related. This is the instruction one would hope for in a private tutorial from the author … The notation is always natural, uncluttered, and helpful. A complete symbol index gives one-line reminders of definitions in addition to page references. Part of the reason the mathematics is so clear is that Kelly's pleasant, simple English exploits fully the power of natural language to describe abstract processes.' Joel E. Cohen, Technometrics '… the main points of the book will be readily grasped by anyone with a knowledge of Markov Chains and processes … It is a good buy for anyone interested in network modelling.' Antony Unwin, Journal of the Operational Research Society '… an important and well-written book that should be in the library of every student of stochastic networks … Among the many appealing features of this book, we note the great diversity of the models to which the results may be applied. There are examples and discussions from genetics, chemical kinetics, queues, migration processes, epidemic theory, and others … The author has a lucid style and has obviously been led by the desire to inform the reader. This, indeed, is also the way to be genuinely impressive.' Marcel F. Neuts, Journal of the American Statistical Association '… a fascinating account of reversibility and its generalisations and consequences, mostly for Markov processes … written in an extremely lucid and clear style … an outstanding book and is essential reading for anyone interested in stochastic processes. Dr Kelly is to be congratulated for producing what is bound to become a standard text.' B. W. Silverman, Journal of the Royal Statistical Society: Series A '… a fascinating and original contribution to probability theory … Anyone with a knowledge of probability theory to the level of Feller's volume I and an interest in stochastic processes is strongly encouraged to read this book.' P. M. Lee, Mathematical Gazette '… an interesting contribution, important from a theoretical as well as an applied point of view … A great number of examples is clearly discussed and analyzed, and as such the book is a nice introduction.' J. W. Cohen, Statistical Neerlandica 'Although the mathematics in this book is elementary, the results are useful and sophisticated.' Frank Spitzer, SIAM Review