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

Singular Integral Equations. By N.I. Muskhelishvili. Translated fromthe 2nd Russian edition by J.R.M. Radok. Pp. 447. F1. 28.50. 1953. (Noordhoff, Groningen)

The present invention is generally directed to a system for monitoring a variety of environmental and/or other conditions within a defined remotely located region. In one aspect, a system is configured to monitor utility meters (613) in a defined area. The system is implemented by using a plurality of wireless transmitters (614), each integrated into a sensor (612) adapted to monitor a particular data input. The system also includes a plurality of transceivers (221) that are dispersed throughout the region at defined locations. The system uses a local gateway (210) to translate and transfer information from the transmitters to a dedicated computer (260) on a network (230). The dedicated computer collects, compiles and stores the data for retrieval upon client demand across the network. The computer further includes means for evaluating the received information and identifying an appropriate control signal to be applied at a designated actuator.

System and method for monitoring and controlling remote devices

Telephone call centers are an integral part of many businesses, and their economic role is significant and growing. They are also fascinating sociotechnical systems in which the behavior of customers and employees is closely intertwined with physical performance measures. In these environments traditional operational models are of great value--and at the same time fundamentally limited--in their ability to characterize system performance.We review the state of research on telephone call centers. We begin with a tutorial on how call centers function and proceed to survey academic research devoted to the management of their operations. We then outline important problems that have not been addressed and identify promising directions for future research.

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Commissioned Paper: Telephone Call Centers: Tutorial, Review, and Research Prospects

Queueing systems in which the server works on primary and secondary (vacation) customers arise in many computer, communication, production and other stochastic systems. These systems can frequently be modeled as queueing systems with vacations. In this survey, we give an overview of some general decomposition results and the methodology used to obtain these results for two vacation models. We also show how other related models can be solved in terms of the results for these basic models. We attempt to provide a methodological overview with the objective of illustrating how the seemingly diverse mix of problems is closely related in structure and can be understood in a common framework.

Queueing systems with vacations—a survey

M/M/1 queues with working vacations (M/M/1/WV)

Processors handling multi-class traffic typically alternate between serving a particular class of traffic and performing other tasks, e.g., secondary service tasks or routine maintenance. The stochastic behavior of such systems is modeled by a newly introduced class of Bernoulli GI/G/1 vacation models. For this model, when a vacation is completed and customers are present, a customer is served. When a customer has just been served and other customers are present, the server accepts a customer with fixed probability p or commences a vacation of prespecified random duration with probability 1 – p. Whenever no customers are present, a vacation is taken. When p = 0 or p = 1 this schedule reduces to the previously introduced single service schedule and the exhaustive service schedule, respectively. An analysis of all three schedules on a state space incorporating server vacations is presented using simple methods in the complex plane. It is shown that the recent decomposition results for exhaustive service extend to the more general class of Bernoulli schedules.

Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules

A wireless communication device using a verification protocol for verifying the identification of the wireless device by a wireless network control station in the presence of eavesdroppers is disclosed. Upon receiving a call request from a wireless device claiming a particular identity, the wireless network control station sends a mask consisting of binary digits in a random order. The wireless device is expected to respond to this mask with a reply that is consistent with both the password contained in the device and the mask. Specifically, the bits of both the password and the mask are "ANDed" and the result transmitted to the wireless network control station as the reply.

Wireless device for verifying identification

Processors handling multi-class traffic typically alternate between serving a particular class of traffic and performing other tasks, e.g., secondary service tasks or routine maintenance. The stochastic behavior of such systems is modeled by a newly introduced class of Bernoulli GI/G/1 vacation models. For this model, when a vacation is completed and customers are present, a customer is served. When a customer has just been served and other customers are present, the server accepts a customer with fixed probability p or commences a vacation of prespecified random duration with probability 1 - p. Whenever no customers are present, a vacation is taken. When p = 0 or p = 1 this schedule reduces to the previously introduced single service schedule and the exhaustive service schedule, respectively. An analysis of all three schedules on a state space incorporating server vacations is presented using simple methods in the complex plane. It is shown that the recent decomposition results for exhaustive service extend to the more general class of Bernoulli schedules.

https://www.jstor.org/stable/info/3214016

Oscillating random walk models for gi/g/1 vacation

For many system contexts for which Little's Law is valid a distributional form of the law is also valid. This paper establishes the prevalence of such system contexts and makes clear the value of the distributional form.

L. D. Servi

Papers

M/M/1 queues with working vacations (M/M/1/WV)

Oscillating random walk models for GI/G/1 vacation systems with Bernoulli schedules

Wireless device for verifying identification

Oscillating random walk models for gi/g/1 vacation

A distributional form of Little's Law