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BOOK REVIEWS 139 this book than what the mathematician is. I believe that this would be an excellent choice for a more advanced course in dynamical systems which emphasized applications. Such a course might have as a prerequisite the material of one of the other books and should be supplemented with some original sources. xii + 308 pp., $37.50. ISBN 0-1266-0650-1. When the early mathematical models of queues were formulated in the beginning of this century, some of the main concepts in the more general field of stochastic processes were not fully developed. Hence these models were at best crude approximations of reality. As more and more tools from the theory of stochastic processes were made available, it was possible to formulate models which were more reahstic descriptions of the actual phenomena under study. As a simple illustration, one may refer to the underlying parameters of a simple queu, which by and large were assumed to be fixed, but more realistically vary in accordance with some underlying random fluctuations such as the queu size. Evidently the analyses of such models were more involved with the end results not being in terms of simple functions, but often involving in some form one or more of the family of functions-known as special functions-i.e., gamma, incomplete gamma, beta, incomplete beta, Bessel, modified Bessel, hypergeometric, etc. What then can be learned from the intersection of the vast amount of literature available in these two areas of mathematics, namely theory of special functions and queuing theory? This well-researched book provides a source for those who attempt to seek answers to this question. Its extensive bibliography lists recent contributions of many authors who have analyzed queuing models which differ from well-known early formulations in that they are often more reahstic descriptions of reahty. Precisely, the authors attempt to demonstrate how and where special functions appear in the analysis of special queuing models.

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