Praise for the Third Edition: "This is one of the best books available. Its excellent organizational structure allows quick reference to specific models and its clear presentation . . . solidifies the understanding of the concepts being presented."IIE Transactions on Operations EngineeringThoroughly revised and expanded to reflect the latest developments in the field, Fundamentals of Queueing Theory, Fourth Edition continues to present the basic statistical principles that are necessary to analyze the probabilistic nature of queues. Rather than presenting a narrow focus on the subject, this update illustrates the wide-reaching, fundamental concepts in queueing theory and its applications to diverse areas such as computer science, engineering, business, and operations research.This update takes a numerical approach to understanding and making probable estimations relating to queues, with a comprehensive outline of simple and more advanced queueing models. Newly featured topics of the Fourth Edition include:Retrial queuesApproximations for queueing networksNumerical inversion of transformsDetermining the appropriate number of servers to balance quality and cost of serviceEach chapter provides a self-contained presentation of key concepts and formulae, allowing readers to work with each section independently, while a summary table at the end of the book outlines the types of queues that have been discussed and their results. In addition, two new appendices have been added, discussing transforms and generating functions as well as the fundamentals of differential and difference equations. New examples are now included along with problems that incorporate QtsPlus software, which is freely available via the book's related Web site.With its accessible style and wealth of real-world examples, Fundamentals of Queueing Theory, Fourth Edition is an ideal book for courses on queueing theory at the upper-undergraduate and graduate levels. It is also a valuable resource for researchers and practitioners who analyze congestion in the fields of telecommunications, transportation, aviation, and management science.

Fundamentals of Queueing Theory

Stable non-Gaussian random processes , by G. Samorodnitsky and M. S. Taqqu. Pp. 632. £49.50. 1994. ISBN 0-412-05171-0 (Chapman and Hall).

Conditional rewriting logic as a unified model of concurrency

Probability and Measure

1. Introduction 2. Background 3. Performance evaluation process algebra 4. Modelling study: multi-server multi-queue systems 5. Notions of equivalence 6. Isomorphism and weak isomorphism 7. Strong bisimilarity 8. Strong equivalence 9. Conclusions Bibliography Index.

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A Compositional Approach to Performance Modelling

Programming parallel machines is notoriously difficult. Factors contributing to this difficulty include the complexity of concurrency, the effect of resource allocation on performance and the current diversity of parallel machine models. The net result is that effective portability, which depends crucially on the predictability of performance, has been lost. Functional programming languages have been put forward as solutions to these problems, because of the availability of implicit parallelism. However, performance will be generally poor unless the issue of resource allocation is addressed explicitly, diminishing the advantage of using a functional language in the first place.

Parallel Programming Using Skeleton Functions

(Each chapter concludes with Exercises.) Preface. 1. Essentials of Probability Theory. Sample space, events and probability. Conditional probability. Independence. 2. Random Variables and Distributions. Probability distribution functions. Discrete random variable. Continuous random variables. Joint random variables. Conditional distributions. Independence and sums. 3. Expected Values and Moments. Expectation. Generating functions and transforms. Asymptotic properties. 4. Stochastic Processes. Random walks. Markov chains. Markov processes. Reversibility. Renewal theory. 5. Queues. Simple Markovian queues. The M/G/1 queue. The G/G/1 queue. 6. Single Class Queueing Networks. Introduction. Open queueing networks. Closed queueing networks. Mean value analysis. Performance measures for the state-dependent case. The flow equivalent server method. 7. Multi-class Queueing Networks. Service time distributions. Types of service centre. Multi-class traffic model. BCMP theorem. Properties and extensions of BCMP networks. Computational algorithms for BCMP networks. Priority disciplines. Quasi-reversibility. 8. Approximate Methods. Decomposition. Fixed point methods. Diffusion approximation. Maximum entropy methods. 9. Time Delays. Time delays in the single server queue. Time delays in networks of queues. Inversion of the Laplace transforms. Approximate methods. 10. Blocking in Queueing Networks. Introduction. Types of blocking. Two finite queues in a closed network. Aggregating Markovian states. BAS blocking. BBS blocking. Repetitive service blocking. 11. Switching Network Models. Telephone networks. Interconnection networks for parallel processing systems. Models of the full crossbar switch. Multi-stage interconnection networks. Models of synchronous MINS. Models of asynchronous MINS. Interconnection networks in a queueing model. Appendix: Outline Solutions. References. Index. 0201544199T04062001

Performance modelling of communication networks and computer architectures

Turning back time in Markovian process algebra

We present a process algebra, SPADES, based on Milner’s CCS, which may be used to describe discrete event simulations with parallelism. It is able to describe the passing of time and probabilistic choice, either discrete, between a countable number of processes, or continuous, to choose a random amount of time to wait. Its operational semantics is presented as a labelled transition system and we discuss equivalences over this operational semantics that imply axioms that can be used to compare and transform processes formally. We discuss notions of equivalence over simulations and the meaning of non-determinism in the context of the specification of a simulation. The algebra is applied to describe quantitatively a range of communicating systems.

SPADES - a process algebra for discrete event simulation

We derive expressions for the generating function of the equilibrium queue length probability distribution in a single server queue with general service times and independent Poisson arrival streams of both ordinary, positive customers and negative customers which eliminate a positive customer if present. For the case of first come first served queueing discipline for the positive customers, we compare the killing strategies in which either the last customer in the queue or the one in service is removed by a negative customer. We then consider preemptive-restart with resampling last come first served queueing discipline for the positive customers, combined with the elimination of the customer in service by a negative customer- the case of elimination of the last customer yields an analysis similar to first come first served discipline for positive customers. The results show different generating functions in contrast to the case where service times are exponentially distributed. This is also reflected in the stability conditions. Incidently, this leads to a full study of the preemptive-restart with resampling last come first served case without negative customers. Finally, approaches to solving the Fredholm integral equation of the first kind which arises, for instance, in the first case are considered as well as an alternative iterative solution method.

Peter G. Harrison

Papers

Parallel Programming Using Skeleton Functions

Performance modelling of communication networks and computer architectures

Turning back time in Markovian process algebra

SPADES - a process algebra for discrete event simulation

The M/G/1 queue with negative customers