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

In this paper, we revisit level-dependent quasi-birth-death processes with finitely many possible values of the level and phase variables by complementing the work of Gaver, Jacobs, and Latouche (Adv. Appl. Probab. 1984), where the emphasis is upon obtaining numerical methods for evaluating stationary probabilities and moments of first-passage times to higher and lower levels. We provide a matrix-analytic scheme for numerically computing hitting probabilities, the number of upcrossings, sojourn time analysis, and the random area under the level trajectory. Our algorithmic solution is inspired from Gaussian elimination, which is applicable in all our descriptors since the underlying rate matrices have a block-structured form. Using the results obtained, numerical examples are given in the context of varicella-zoster virus infections.

https://www.mdpi.com/2227-7390/8/10/1718/pdf

On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics

Queueing networks with blocking have broad applications in computer modelling and manufacturing. The present paper focusses on the MMAP[2]/M/1/ ∞ →·/M/1/K + 1 G-queue with blocking. This network consists of a sequence of two single-server stations with an infinite queue allowed before the first server and an intermediate queue of finite capacity K ≥ 0 allowed between servers. This restriction results in the blocking of the first server whenever a unit having completed its service in Station 1 cannot enter into Station 2 due to K + 1 units are accommodated into Station 2. There are two types of arrivals, called units and signals, which are modelled by a single Markovian arrival process with marked transitions. Each unit is served at Stations 1 and 2 in that order, and then it exits of the network. A signal induces the last unit in queue or in service, if there is one, to leave the network instantly, and it has no effect otherwise. Our purpose is to study the influence of the dependence between units and signals on the performance evaluation of the continuous-time Markov chain describing the state of the network at arbitrary times, which constitutes a quasi-birth-and-death process. We present tractable formulas for a variety of probabilistic descriptors, with special emphasis on the distribution of inter-departure times.

Marked Markovian Arrivals in a Tandem G-Network with Blocking

Bayesian inference methods are illustrated for the most relevant Markovian processes: discrete and continuous time Markov chains, Poisson processes, discrete time continuous space Markov processes, and diffusion processes. Examples from biology, ecology, finance, and queueing motivate the discussion.


Keywords:

Markov chain;
Markov process;
Poisson process;
diffusions;
Bayesian analysis

https://onlinelibrary.wiley.com/doi/pdf/10.1002/9781118445112.stat07837

Bayesian Inference of Markov Processes

Modeling host-parasitoid interactions with correlated events

In telecommunications, packets or units may complete their service in a different order from the one in which they enter the station. In order to reestablish the original order resequencing protocols need to be implemented. In this article, the focus is on a two-server resequencing system with heterogeneous servers and two buffers. One buffer has an infinite capacity to hold the incoming units. The other with a finite capacity is used to resequence the serviced units. This is to maintain the order of departure of the units according to the order of their arrivals. To analyze this resequencing model, we introduce an equivalent two-stage queueing system, namely A. B. Clarke's Tandem Queue, in which the arriving units receive service from only one server, and the units departing from the first stage may be temporally prevented from leaving by occupied service units at the second stage. Our interest is to study the resequencing delay and the sojourn time as times until absorption in suitably defined quasi-birth-and-death processes and continuous-time Markov chains.

Antonio Gómez-Corral

Papers

On First-Passage Times and Sojourn Times in Finite QBD Processes and Their Applications in Epidemics

Marked Markovian Arrivals in a Tandem G-Network with Blocking

Bayesian Inference of Markov Processes

Modeling host-parasitoid interactions with correlated events

A. B. Clarke's Tandem Queue Revisited—Sojourn Times