First published in 1979, this book immediately attracted the attention of specialists in applied probability and stochastic processes. Today, it is a classic in reversibility of stochastic processes and its applications.

The notion of reversibility was introduced by Kolmogorov in 1930. According to his definition, a stochastic process, X(t), is called reversible if finite-dimensional distributions of X(t) and X(-t) are the same. It follows immediately from the definition that reversible processes are stationary.

The simplest examples of reversible processes are provided by the birth and death process with a finite number of states. They have huge numbers of applications because of their analytical tractability. These examples are considered in chapter 1, which includes a detailed analysis of the famous Ehrenfest model describing the apparent paradox between reversibility and the phenomenon of increasing entropy.

Chapter 2 addresses migration processes. It contains important results for the analysis of open and closed queues. Among these queueing systems, special attention is paid to the systems having so-called product form distributions. This property appeared to be connected to the reversibility of the stochastic networks and the preservation of Poisson flow. Chapters 3 and 4 continue the analysis of examples of queueing networks, including communication networks, teletraffic models, and machine interference. The last topic is very important in performance analysis of computer systems.

A connection between reversible random walks and electrical networks is discussed in chapter 5, and chapter 6 covers an interesting model of social behavior. Chapter 7 presents applications of reversible processes in population genetics. Here, the reader will become familiar with the model providing insight into the behavior of populations subject to recurrent neutral mutation.

Examples related to the field of polymer chemistry are considered in chapter 8, and spatial processes are discussed in chapter 9. The processes considered in these chapters represent multivariate generalizations of the migration processes considered in chapter 2. Spatial processes are capable of describing multi-component systems. They belong to a special class of Markov fields.

Each chapter contains a large number of problems and exercises, which contain many important results that can be found only in special papers on queueing theory.

The book is written in a very precise and elegant manner. It starts with elementary ideas and leads the reader into a very rich world of ideas and applications of reversible stochastic processes in the areas of operations research, management sciences, biological and chemical modeling, and social sciences. The reader will need only a good understanding of elementary probability to enjoy this book.