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

OR/MS research in disaster operations management

Applied Probability and Queues.

https://link.springer.com/content/pdf/10.1057%2Fjors.1996.159.pdf

Modeling and Analysis of Stochastic Systems

The application of auto-repeat facilities in telephone systems, as well as the use of random access protocols in computer networks, have led to growing interest in retrial queueing models. Since much of the theory of retrial queues is complex from an analytical viewpoint, with this book the authors give a comprehensive and updated text focusing on approximate techniques and algorithmic methods for solving the analytically intractable models.

Retrial Queueing Systems: A Computational Approach also

 * Presents motivating examples in telephone and computer networks.
 * Establishes a comparative analysis of the retrial queues versus standard queues with waiting lines and queues with losses.
 * Integrates a wide range of techniques applied to the main M/G/1 and M/M/c retrial queues, and variants with general retrial times, finite population and the discrete-time case.
 * Surveys basic results of the matrix-analytic formalism and emphasizes the related tools employed in retrial queues.
 * Discusses a few selected retrial queues with QBD, GI/M/1 and M/G/1 structures.
 * Features an abundance of numerical examples, and updates the existing literature.

The book is intended for an audience ranging from advanced undergraduates to researchers interested not only in queueing theory, but also in applied probability, stochastic models of the operations research, and engineering. The prerequisite is a graduate course in stochastic processes, and a positive attitude to the algorithmic probability.

Retrial Queueing Systems: A Computational Approach

A structured Markov chain model to investigate the effects of pre-exposure vaccines in tuberculosis control.

The literature on queueing systems with state-dependent parameters includes a variety of features, such as finite populations, server vacations, variable service rates, queue length dependence, retrials, and control of the admission upon arrival. The complexity of the stochastic models obtained by combining these non-homogeneous features and the method of stages causes practical difficulties. From the point of view of the numerical implementation, the large dimensionality of the underlying matrix representations is a serious problem that requires attention. Specifically, this is a key aspect if an arbitrary, even infinite number of Markovian arrival processes and phase-type distributions are involved. These considerations on the inherent difficulties associated with the stochastic modeling of block-structured state-dependent (BSDE) Markov chains provide the motivation for our study. In this paper, we briefly present the BSDE approach to construct either a specific part or the whole stochastic system in continuous time, modeling a state-dependent phenomenon operating in the presence of phases. A variant of the approach also holds in discrete time. We focus on the correlation structure and present two measures of correlation between events.

Markov chains with block-structured state-dependent events: formulation and correlation analysis

We consider an M/G/1 retrial queue with finite capacity of the retrial group. We derive the Laplace transform of the busy period using the catastrophe method. This is the key point for the numerical inversion of the density function and the computation of moments. Our results can be used to approach the corresponding descriptors of the M/G/1 queue with infinite retrial group, for which direct analysis seems intractable.

Antonio Gómez-Corral

Papers

A structured Markov chain model to investigate the effects of pre-exposure vaccines in tuberculosis control.

Markov chains with block-structured state-dependent events: formulation and correlation analysis

A Note On The Busy Period Of The M / G /1 Queue With Finite Retrial Group

Selected Retrial Queues with QBD Structure

Selected Retrial Queues with GI/M/1 and M/G/1 Structures