European Institute for Statistics, Probability, Stochastic Operations Research and its Applications

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Queueing phenomena occur in several real-life situations when resources (machines at a factory, elevators, telephone lines, traffic lights) cannot immediately render the amount or the kind of service required by their users. Similar congestion phenomena also arise at the byte level, in modern data-handling technologies (communication systems, computer networks); they are typically less visible but their effects at user level are usually not less serious. Such congestion phenomena are often very effectively studied by mathematical methods from queueing theory. Adopting the abstract terminology from queueing theory, the object of study is formulated as a network of service units with customers requiring services at those units. The nature of the arrival and service processes is usually such that they have to be represented by stochastic processes. Accordingly, queueing theory is an area of applied probability theory and of stochastic operations research. 

Queueing theory is an extremely active area of research. One of the key reasons for its strong viability is that, time and again, interesting new questions from, mainly, computer-communications and manufacturing give rise to new and challenging queueing problems. Much research is being triggered by the need to understand and control the behaviour of modern computer-, communication- and manufacturing systems, and thus to improve their design and performance.

Information and communication technology is a vital sector in today's world economy. The future development of this field strongly depends on contributions from mathematics. In the early stages of this development in the design of computer-communication systems, the emphasis was on functionality. In recent years quality of service has become the most important criterion, which is expressed in terms of performance and reliability of the systems in relation to telematics applications. Queueing networks also provide the models for the description of manufacturing systems and for the analysis of their performance and reliability aspects. These economically vital applications of queueing networks make them into objects that are of prime interest.

The goal of the QPA programme is to give a strong impetus to the analysis of queueing systems and their applicability to the performance analysis of computer-, communication- and production networks. The programme focuses on three themes:

  • Queueing Theory

  • Performance Analysis of Production Systems

  • Performance Analysis of Communication Systems

The QPA group keeps close ties with the Stochastic Operations Research group (SOR) at the Department of Mathematics and Computer Science of Eindhoven University of Technology (TU/e). Several members of the latter group are involved in the activities of the project, including Ivo Adan, Sem Borst, Onno Boxma, Johan van Leeuwaarden, Jacques Resing and Jan van der Wal, as well as a number of PhD students. There are also several interactions with researchers from the Department of Technology Management and Mechanical Engineering at TU/e, with Michel Mandjes at Uva and CWI, Richard Boucherie's group at the University of Twente, and other institutes.

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