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

http://gljc.sxu.edu.cn/docs/2013-11/20131129080455222534.pdf

The discrete-time GI/Geo/1 queue with working vacations and vacation interruption

1. Explain why difference equations result from digital control of analog systems. 2. Obtain the z-transform of a given time sequence and the time sequence corresponding to a function of z. 3. Solve linear time-invariant (LTI) difference equations using the z-transform. 4. Obtain the z-transfer function of an LTI system. 5. Obtain the time response of an LTI system using its transfer function or impulse response sequence. 6. Obtain the modified z-transform for a sampled time function. 7. Select a suitable sampling period for a given LTI system based on its dynamics. Digital control involves systems whose control is updated at discrete time instants. Discrete-time models provide mathematical relations between the system variables at these time instants. In this chapter, we develop the mathematical properties of discrete-time models that are used throughout the remainder of the text. For most readers, this material provides a concise review of material covered in basic courses on control and system theory. However, the material is self-contained, and familiarity with discrete-time systems is not required. We begin with an example that illustrates how discrete-time models arise from analog systems under digital control.

Discrete-time systems

An M/G/1 queue with single working vacation and vacation interruption under Bernoulli schedule

https://ir.nctu.edu.tw:443/bitstream/11536/5405/1/000276790000018.pdf

Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation

The discrete time Geom/Geom/1 queue with multiple working vacations

We study a discrete-time Geom/Geom/c/c Erlang loss system. In this queueing system, we give the function equation that the generating function of the number of customers satisfies in steady-state system, and get the formula of stationary mean queue length. Furthermore, we derive recursive method to compute stationary queue length probability and loss probability. Finally, using a numerical example, we exemplify the relation between loss probability, the mean number of customers and various parameters

Performance Analysis of Discrete-Time Erlang Loss System

Abstract In this paper, an M/G/1 queue model with the multiple adaptive vacations and pure decrementing service policy is studied based on the classical M/G/1 queueing model. The PGF of stationary queue length is derived by using an embedded Markov chain method. The LST of stationary waiting time is also given according to the independence between waiting time and arrival process. The average probabilities of various system states are obtained. Some special cases are given to show the general properties of the new model.

Pure Decrementing Service M/G/1 Queue with Multiple Adaptive Vacations

We consider a Geom/G/1 gate service system with multiple adaptive vacation based on the classical Geom/G/1 queueing system. By using regeneration cycle approach, we obtain the PGF(Probability Generating Function) of the stationary queue length. Because of the independent property of the waiting time and the arrival process after its arrival, the PGF of the stationary waiting time is derived. Finally we obtain the average probabilities of various system state, some special cases are given to show the new model's general properties.

A geom/G/1 gate service system with multiple adaptive vacation

The study of vacation queue started in the 1970s. Up to now, it has made abundant achievements, formed a theoretical framework with stochastic decomposition as the core, and has been applied to many fields. This paper gives a comprehensive overview of the research results and analysis methods of vacation queue, including its applications in the communication networks.

Zhanyou Ma

Papers

The discrete time Geom/Geom/1 queue with multiple working vacations

Performance Analysis of Discrete-Time Erlang Loss System

Pure Decrementing Service M/G/1 Queue with Multiple Adaptive Vacations

A geom/G/1 gate service system with multiple adaptive vacation

A Survey for Stochastic Decomposition in Vacation Queues