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

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

Modelling and optimization for cognitive radio networks with preemption backoff mechanism

In this paper we model the base station of multi-channel mobile communication systems with finite user population discrete time queueing system. Using the method of Markov chain we derive the performance index such as probability of loss in one slot, the average throughput of the system, and the utilization ratio of channels. And through the numerical simulation, we discuss the effect of the model to the multi-channel mobile communication systems.

Performance Analysis of Multi-channel Mobile Communication Systems Based on Discrete Time Queue

Voice over Internet Protocol (VoIP) or Internet telephony has become an evolutionary and promising technology in the area of telecommunications. Lower costs and simpler maintenance are the major reasons of its increasing popularity. However, the network is inherently unreliable and highly challenged when it comes to quality of service (QoS). The VoIP system is primarily a multi-server system which may also face failures. Hence, in order to study the performance of VoIP, it is proposed to develop a multi-server, loss system with general service times, server breakdown and repair together with preemptive priority queuing discipline, for two types of customers: high priority and low priority. The customers are served immediately if the server is available. However, if all servers are busy, then on the arrival of a high priority customer, the service of a low priority customer is preempted. The steady state distribution of such underlying system is obtained together with the performance measures. A numerical illustration of the obtained results is also presented graphically. The results are validated using simulation.

https://web.iitd.ac.in/~dharmar/paper/Opsearch2014.pdf

Performance analysis of voice over internet protocol via non Markovian loss system with preemptive priority and server break down

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

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.

A Survey for Stochastic Decomposition in Vacation Queues

In this paper, an admission control scheme with priority for real-time traffic is designed, and a discrete time Geo1 +larr Geo2/Geo1,Geo2/s (preemptive priority) queue model is proposed to study the performance of the multi-traffic admission control scheme, which based on the running mechanism of the wireless multi-channel communication network and the various quality of service (QoS) requirement of multitraffic. Using matrix-geometric solution method, we get the performance measure, such as, average queue length for both traffic, blocking probability of real-time traffic and utilization rate of channel. And computer simulations verify the accuracy of the model

Xiuli Xu

Papers

Performance Analysis of Discrete-Time Erlang Loss System

A Survey for Stochastic Decomposition in Vacation Queues

Admission Control for Multi-Traffic in Wireless Multi-Channel Communication Network Based on Discrete Time Queue