Synopses & Reviews
The textbook contains the records of a two-semester course on queueing theory, including an introduction to matrix-analytic methods. The course is directed to last year undergraduate and first year graduate students of applied probability and computer science, who have already completed an introduction to probability theory. Its purpose is to present material that is close enough to concrete queueing models and their applications, while providing a sound mathematical foundation for their analysis. A prominent part of the book will be devoted to matrix-analytic methods. This is a collection of approaches which extend the applicability of Markov renewal methods to queueing theory by introducing a finite number of auxiliary states. For the embedded Markov chains this leads to transition matrices in block form resembling the structure of classical models. Matrix-analytic methods have become quite popular in queueing theory during the last twenty years. The intention to include these in a students' introduction to queueing theory has been the main motivation for the authors to write the present book. Its aim is a presentation of the most important matrix-analytic concepts like phase-type distributions, Markovian arrival processes, the GI/PH/1 and BMAP/G/1 queues as well as QBDs and discrete time approaches.
Review
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)
Synopsis
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."
Table of Contents
List of Figures. Foreword.- Queues: The Art of Modelling.- Part I: Markovian Methods. Markov Chains and Queues in Discrete Time. Homogeneous Markov Processes on Discrete State Spaces. Markovian Queues in Continuous Time. Markovian Queueing Networks.- Part II: Semi-Markovian Methods. Renewal Theory. Markov Renewal Theory. Semi-Markovian Queues.- Part III: Matrix-Analytic Methods. Phase-Type Distributions. Markovian Arrival Processes. The GI/PH/1 Queue. The BMAP/G/1 Queue. Discrete Time Approaches. Spatial Markovian Arrival Processes. Appendix.- References.- Index.