The present textbook contains the recordsof a two-semester course on que- ing theory, including an introduction to matrix-analytic methods. This course comprises four hours oflectures and two hours of exercises per week andhas been taughtattheUniversity of Trier, Germany, for about ten years in - quence. The course is directed to last year undergraduate and?rst year gr- uate students of applied probability and computer science, who have already completed an introduction to probability theory. Its purpose is to present - terial that is close enough to concrete queueing models and their applications, while providing a sound mathematical foundation for the analysis of these. Thus the goal of the present book is two-fold. On the one hand, students who are mainly interested in applications easily feel bored by elaborate mathematical questions in the theory of stochastic processes. The presentation of the mathematical foundations in our courses is chosen to cover only the necessary results, which are needed for a solid foundation of the methods of queueing analysis. Further, students oriented - wards applications expect to have a justi?cation for their mathematical efforts in terms of immediate use in queueing analysis. This is the main reason why we have decided to introduce new mathematical concepts only when they will be used in the immediate sequel. On the other hand, students of applied probability do not want any heur- tic derivations just for the sake of yielding fast results for the model at hand.

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From the reviews:

"This book provides a mathematical introduction to the theory of queuing theory and matrix-analytic methods ... . The style of the text ... is concise and rigorous. The proofs are presented for study. Each chapter concludes with a set of exercises inviting readers to prove supplementary results and review particular aspects of the theory. ... I have found this to be a useful reference text and would recommend it to those wishing to delve into the mathematical theory of basic queuing theory." (Michael NG, SIAM Review, Vol. 48 (3), 2006)

"The book under review attempts to give an introduction to the theory of queues without losing contact with its applicability. ... For instructors who prefer the topics covered, this book is a nice candidate as they do not need to choose the topics but only need to elaborate on them. Nevertheless, it would be a good reference book for an introductory course in queuing theory, stochastic modelling, or applied probability, and a valuable one to add to a professional’s bookshelf." (N. Selvaraju, Mathematical Reviews, Issue 2007 c)

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