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

Discrete-time analysis of two schemes for multiplexing voice and data is presented. In each scheme voice and data are multiplexed using the movable boundary frame allocation scheme. In the first scheme, speech activity detectors (SAD's) are not used, and hence, the variations in the voice traffic are only due to the on/off characteristics of voice. In the second scheme, SAD's are employed so that talker silences can he utilized for transmission of additional voice and/or data. In this scheme, the multiplexer performs digital speech interpolation as well as movable boundary frame allocation. The performance measures considered are probability of loss for voice calls, probability of speech clipping, speech packet rejection ratio, and the expected data message delay. In the case of the multiplexer with SAD, a tradeoff exists between data message delay and speech interpolation advantage. Some numerical examples are presented which illustrate the performance of the two multiplexers.

Discrete-Time Analysis of Integrated Voice/Data Multiplexers With and Without Speech Activity Detectors

Data queueing is of primary concern in a voice/data integrated TDM system. The data queueing model is represented in the discrete-time domain with multiple servers and voice is given a higher priority than data. The data arrival process is assumed to be Poisson and the voice arrival process is characterized by a Markov chain. The correlation coefficient of the number of on voice calls between consecutive frames is used to measure the correlation behavior of the voice process. While the generating function approach may be used to analyze the queueing process, it involves the evaluation of a large number of boundary terms. On the assumption that the voice traffic consists of N i.i.d. two-state Markov chains, we derive a simple expression for the mean queue size as a function of two variables in the form of the traffic departure processes. The results clearly reveal a significant influence of the correlation coefficient on the data queueing process. Then, an approximate analysis based on the departure processes is introduced. The numerical and simulation results indicate that this approximate approach yields reasonably accurate results.

Performance of Voice/Data Integration on a TDM System

An approach to the analysis of overload control in a finite buffer is introduced in which the original queuing process is modeled by a birth-and-death (BD) or quasi-birth-and-death (QBD) process. Overload control means to adapt the input process or the service process during the time period when the buffer content exceeds a certain level until it drops to another level. Such a control is necessary to reduce the occurrence of system shutdown periods and to protect high-priority messages against low-priority ones. Since the controlled process two be computed in terms of the will no longer be BD or QBD, the methodology commonly used for analyzing BD or QBD process cannot be applied. This makes direct analysis and computation of the controlled performance more complicated. The analytical methods consists in dividing the controlled process into two altering transient BD or QBD subprocesses, by observing only some selected transitions. Such a division enables the equilibrium probabilities of the controlled process to be computed in terms of the sojourn times of the two transient processes. It is shown that this is equivalent to the analysis and computation of equilibrium probabilities of the underlying stationary BD or QBD process. >

Overload control in a finite message storage buffer

A discrete-time queuing analysis is presented for integration of multiple traffic types in a packet-switched TDM (time-division multiplexing) system. The correlation of each traffic type is represented in terms of the power spectral density. The general expression obtained for the aggregate mean queue size indicates that slowly varying traffic types exert the largest effect on the queuing process. Also, a lengthy-steady traffic is highly predictable. An adaptive flow control and routing scheme, based on signal prediction, which successively adjusts the short-burst traffic arrival rate at each TDM node, is introduced and analyzed. The analytical results indicate a substantial reduction in the correlation effect on the system queuing behavior. >

Traffic characterization for integrated services networks

This paper presents an approximation method for estimating the average number of data packets in a SENET-concept integrated voice and data system. The method is simple to use and its estimates are found to be in good agreement with simulation results. In general, the method applies to any system that integrates packet traffic with a more slowly varying traffic class that can preempt a portion of the packet transmission capacity.

R. Kwong

Papers

Performance Evaluation Methods for an Integrated Voice/Data Link