Introduction to Queueing Theory

This is a text book suitable for 3rd year mathematics graduates and perhaps graduate students of Operational Research. It starts from the basis of an intuitive analysis of a telephone system comprising two cities interconnected by a group of five telephone trunks and applying the principal formulae (which incidentally are proved more rigorously later). Many of the processes considered are those first studied by Erlang and as such are well covered in many books. The chapter reviewing probability topics, which occurs early in the book and discusses birth and death processes and some probability distributions, contains much of relevance to students of queueing theory and some important references. However, having pointed out that P.G.F.s are holomorphic functions within and on the unit circle, the book gives no examples of the use of complex variable theory in the analysis. On the other hand, the explanation of Riemann-Stieltjes integrals and Laplace-Stieltjes transforms, though modest, was informative and is followed by the standard imbedded Markov chain models. Numerous examples are given at the end of each chapter, and the publishers have available an instructor's manual containing detailed solutions. The book contains a bibliography of "almost all the English language" books on queueing theory, and this is useful. Of course, most of the topics studied in this book are contained in the others. From the Operational Research point of view there are no practical examples and little indication of how the theory may be used. Nevertheless, the book is a good introduction to queueing theory and contains worthwhile material and references brought together in one volume.