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

Performance of two-stage tandem queues with blocking: the impact of several flows of signals

Algorithmic analysis of the Geo/Geo/c retrial queue

In this paper, we model a single-server retrial queue with quasi-random input and two priority classes. In the case of blocking, a high priority unit is queued, whereas a low priority unit joins the orbit to start generating a Poisson flow of repeated attempts until it finds the server free. Since units in orbit will be served only when the high priority queue is empty, high priority units have nonpreemptive priority over low priority units. We present a simple analysis for the outside observer distribution of the system state as well as for the arriving unit distribution in steady state. Besides, we give numerical examples to illustrate the effect of the parameters on several performance characteristics.

Analysis of a single-server retrial queue with quasi-random input and nonpreemptive priority☆

The M/M/r/r-d queue with constant retrial rate has many important applications in teletraffic theory and computer and communication networks. An analytical solution of this queue is difficult and would not necessarily lend itself to numerical implementation in the case r+≥ 3. In this paper, we extend the decomposition formulae for the stationary distributions of the standard M/M/r/r+d queue to the M/M/r/r+d queue with constant retrial rate. In the case r+< 3, we show that the stationary distributions of the number of customers in orbit and the total number of servers and waiting positions occupied can be expressed as mixtures of two random variables weighted by the probability of entering the orbit. In the case r+≥ 3, we propose and heuristically explore decomposition formulae for the stationary distribution of the number of customers in orbit

Some decomposition formulae for M/M/r/r+d queues with constant retrial rate

We consider the stochastic behaviour of a Markovian bivariate process {(C(t), N(t)), t≥0} whose statespace is a semi-stripS={0,1}×ℕ. The intensity matrix of the process is taken to get a limit distributionP ij =limt→+∞P{(C(t), N(t))=(i, j)} such that {P0j,j ∈ ℕ}, or alternatively {P1j,j ∈ ℕ}, satisfies a system of equations of ‘birth and death’ type. We show that this process has applications to queues with repeated attempts and queues with negative arrivals. We carry out an extensive analysis of the queueing process, including classification of states, stationary analysis, waiting time, busy period and number of customers served.

Antonio Gómez-Corral

Papers

Performance of two-stage tandem queues with blocking: the impact of several flows of signals

Algorithmic analysis of the Geo/Geo/c retrial queue

Analysis of a single-server retrial queue with quasi-random input and nonpreemptive priority☆

Some decomposition formulae for M/M/r/r+d queues with constant retrial rate

Generalized birth and death processes with applications to queues with repeated attempts and negative arrivals