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

The paper explores the dynamics of extreme values in an SIR (susceptible → infectious → removed) epidemic model with two strains of a disease. The strains are assumed to be perfectly distinguishable, instantly diagnosed and each strain of the disease confers immunity against the second strain, thus showing total cross-immunity. The aim is to derive the joint probability distribution of the maximum number of individuals simultaneously infected during an outbreak and the time to reach such a maximum number for the first time. Specifically, this distribution is analyzed by distinguishing between a global outbreak and the local outbreaks, which are linked to the extinction of the disease and the extinction of particular strains of the disease, respectively. Based on the mass function of the maximum number of individuals simultaneously infected during the outbreak, we also present an iterative procedure for computing the final size of the epidemic. For illustrative purposes, the twostrain SIR-model with cross-immunity is applied to the study of the spread of antibiotic-sensitive and antibiotic-resistant bacterial strains within a hospital ward.

Extreme values in SIR epidemic models with two strains and cross-immunity

The paper deals with a special bivariate Markov process which can be considered as the joint process of the channel (server) state and the number of customers in the orbit of a Markovian single server retrial system with state dependent intensities Several retrial queues, analysed in the literature, are special cases in view of the versatility
of the process Necessary and sufficient conditions for the regularity, ergodicity and recurrence of the process are given For the stationary distribution a product formula
is derived Further the busy period, the number of served customers and other related quantities are studied

On a bivariate Markov process arising in the theory of single‐server retrial queues

The model considered in this paper involves a tandem queue consisting of a sequence of two waiting lines The main feature of our model is blocking, ie, as soon as the second waiting line reaches a certain upper limit, the first line is blocked The input of units to the tandem queue is the MAP (Markovian arrival process), and service requirements are of phase type Our objective is to study the sojourn time distribution under the first-come-first-serve discipline by analyzing the sojourn time through times until absorption in appropriately defined quasi-birth-and-death processes and continuous-time Markov chains

Antonio Gómez-Corral

Papers

Extreme values in SIR epidemic models with two strains and cross-immunity

On a bivariate Markov process arising in the theory of single‐server retrial queues

Sojourn times in a two-stage queueing network with blocking

Information theoretic analysis for queueing systems with quasi-random input

Performance analysis of a single-server queue with repeated attempts