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

Numerical techniques for modeling computer networks under nonstationary conditions are discussed, and two distinct approaches are presented. The first approach uses a queuing theory formulation to develop differential equation models which describe the behavior of the network by time-varying probability distributions. In the second approach, a nonlinear differential equation model is developed for representing the dynamics of the network in terms of time-varying mean quantities. This approach allows multiple classes of traffic to be modeled and establishes a framework for the use of optimal control techniques in the design of network control strategies. Numerical techniques for determining the queue behavior as a function of time for both approaches are discussed and their computational advantages are contrasted with simulation. >

Numerical methods for modeling computer networks under nonstationary conditions

The quality of the service provided by the World Wide Web, namely convenient access to a tremendous amount of information in remote locations, depends in an important way on the time required to retrieve this information. This time in turn depends on a number of parameters, in particular the load at the server and in the network. Overloads are avoided by carefully dimensioning the server (so that it has enough resources such as CPU power and disk space to handle expected requests) and the network (so that it has enough resources such as bandwidth and buffers to transport requests and replies), and by using mechanisms such as caching that minimize the resource requirements of user requests. In this paper, we consider performance issues related to dimensioning and caching. Our contribution is twofold. Regarding dimensioning, we advocate the use of time series analysis techniques for Web traffic modeling and forecasting. We show using experimental data that quantities of interest such as the number of Web requests handled by a server, or the amount of data retrieved per hour by a server, can be accurately modeled with time series such as seasonal ARIMA models. We then use these models to make medium-term predictions of client requests characteristics (number of such requests and size of document retrieved), which in turn can be used as a basis for dimensioning decisions. Regarding caching, we advocate the use of novel cache replacement algorithms that explicitly take document size and network load into account so as to minimize the retrieval time perceived by clients.

Performance engineering of the World Wide Web: application to dimensioning and cache design

A distributed microcellular architecture based on the IEEE 802.6 Metropolitan Area Network (MAN) is proposed, and is shown to meet anticipated personal communications service (PCS) needs. A method is presented to calculate MAN coverage in urban areas, and is used to demonstrate coverage of approximately 50 city blocks per MAN. A distributed subscriber database architecture is proposed to facilitate call setup, tracking of roamers and handoffs. To fully utilize MAN bandwidth, a quick method for the heat stations to switch on/off isochronous slots is proposed to facilitate adaptation to PCS traffic level variations. Call setup and handoff procedures are detailed. The PCS signaling overhead is calculated to be 15% of the capacity required to carry voice traffic. >

Network architecture and signaling for wireless personal communications

A unified framework for traffic control and bandwidth management in ATM networks is proposed. It bridges algorithms for real-time and data services. The central concept of this framework is adaptive connection admission. It employs an estimation of the aggregate equivalent bandwidth required by connections carried in each output port of the ATM switches. The estimation process takes into account both the traffic source declarations and the connection superposition process measurements in the switch output ports. This is done in an optimization framework based on a linear Kalman filter. To provide a required quality of service guarantee, bandwidth is reserved for possible estimation error. The algorithm is robust and copes very well with unpredicted changes in source parameters, thereby resulting in high bandwidth utilization while providing the required quality of service. The proposed approach can also take into account the influence of the source policing mechanism. The tradeoff between strict and relaxed source policing is discussed.

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A framework for bandwidth management in ATM networks—aggregate equivalent bandwidth estimation approach

Discrete-time stochastic models designed to encompass various sequential measurements of telephone traffic are derived from assumptions of classical queueing theory. The models are linear and their coefficients depend on the measurement cycle length normalized by the mean holding time. Proposed descriptions are tested against the real data gathered by the supervisor of the French toll network. Forecasting methods are then proposed and implemented in the simulator of a testbed network with adaptive routing. Simulation results confirm the benefits of advanced routing concepts and allow us to classify various information patterns from the standpoint of their usefulness for traffic control.

Modeling and Prediction of Traffic Fluctuations in Telephone Networks

The presented paper is concerned with qualitative and quantitative analysis of advanced traffic control concepts. In the first part a survey of traffic control techniques is made with the final aim of separating the factors influencing the network grade of service. The second part is devoted to the performance evaluation of adaptive routing in two trial networks. The simulation is used to highlight the significance of network structure, signalling techniques, multiple overflows and update cycle length for the efficiency of a flexible routing rule.

Analysis and control of traffic routing in circuit-switched networks

The evolution of circuit-switched networks is analyzed with respect to the functional innovations that allowed for new traffic controls. The technical alternatives for routing techniques and their integration with congestion and flow control are considered. The performance of dynamically controlled networks is analyzed in the framework of research done at the Centre National d'Etudes des Telecommunications (CNET) together with studies carried out in other research laboratories. Comparisons are made of dynamic routing versus fixed hierarchical routing and time-dependent routing versus adaptive routing. For adaptive routing, centralized and isolated methods are compared. The benefits of advanced control methods are summarized. >

Performance issues in the design of dynamically controlled circuit-switched networks

Kalman Filtering of Traffic Fluctuations for Real-Time Network Management

Discrete- time stochastic models of sequential traffic records in telephone networks are considered. They appear to be well suited for a use of the Kaiman filter. A version of the filtering algorithm is adopted to deal with traffic fluctuations. The overall approach is tested against the real data gathered by the supervisor of the French toll network. The adaptive traffic estimator is inserted into a simulator of a testbed network operated in the urban zone of Paris. The traffic estimations provided by the filter are used to decide an overflow hierarchy.

Janusz Filipiak

Papers

Modeling and Prediction of Traffic Fluctuations in Telephone Networks

Analysis and control of traffic routing in circuit-switched networks

Performance issues in the design of dynamically controlled circuit-switched networks

Kalman Filtering of Traffic Fluctuations for Real-Time Network Management

Kalman filtering of traffic fluctuations for real-time network management