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Queueing analysis. A foundation of performance evaluation. Volume 1: Vacation and priority systems, part 1. (English) Zbl 0744.60114
Amsterdam etc.: North-Holland. xi, 487 p. (1991).
This volume presents a comprehensive analysis of vacation and priority models of single server queues with infinite capacity. Queueing systems where the server sometimes takes a vacation (or serves elsewhere) arise in many computer and communication systems and for this reason the author uses the term ‘messages’ instead of ‘customers’. It is always assumed that the arrival epochs of any one type of message form a Poisson stream and that the service times are independent. The service disciplines include ‘First come first served’, ‘Last come first served’ and ‘Random order of service’. Major part of the analysis is devoted to describe the steady state distributions of random variables such as queue size, waiting time, busy period and interdeparture times. The techniques employed include imbedded Markov chains, semi-Markov processes, renewal theory and the method of supplementary variables.
The book is divided into three large charge chapters each with seven to eight sections. Chapter 1 contains the analysis of the usual \(M/G/1\) systems, which is the basis of all the models presented. Systems with batch arrivals are also presented. The last section deals with the study of message and time dependent processes. Chapter 2 deals with \(M/G/1\) systems with vacations and begins with a summary of generalized vacation models. The next three sections present a variety of exhaustive service systems (where a vacation begins only when there are no messages in the system). The remaining sections deal with gated, limited and decrementing service systems which are non-exhaustive service systems (where a vacation can start even when messages are present in the system). Chapter 3 is devoted to the study of \(M/G/1\) systems with multiple classes which are mostly priority classes. The first section presents the stationary results of queues with multiple classes. The rest of the sections deal with the analysis of priority queues and include non-preemptive and preemptive priority systems, systems with vacations, priority queues with batch arrivals, reservation priority queues and exhaustive priority queues.
Each chapter is accompanied by an extensive list of its own specific references. In addition, a bibliography listing books on queues and telegraphic engineering and selected books on stochastic processes containing material on queueing theory is given. A glossary of notation is also provided.
This book is very useful for students and researchers in Operations Research, Computer Science and Industrial Engineering, particularly those working in the field of queueing theory.

60K25 Queueing theory (aspects of probability theory)
60-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to probability theory
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B22 Queues and service in operations research