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Algorithmic Analysis of Queues

It is my feeling that at present queueing theory is divided into two directions. One is highly abstract and the other highly practical. It seems that this split will continue to grow wider and wider. Progress in the theory of stochastic processes (especially point, regenerative, and stationary processes) will influence new approaches to queueing theory. This may be in the form of new methods, new interpretations, and the development of new theories with wide applicability. Researchers in abstract probability usually do not have queueing theory in mind; different talents are required to find applicability of their results. Other examples, are diffusion approximation, the large deviations technique, and random fields. One may hope that the near future will bring applications of superprocesses, the object of current research in stochastic processes. Progress in technical developments of systems involving various forms of traffic created the need for mathematical analysis of performance of individual systems. This brings new problems which require new tools, and the search for these tools is of great practical importance. This is clearly visible not only in teletraffic theory, but also in other disciplines where queueing methods are used (biological and health studies, computers). As already mentioned, simulation and numerical analysis are frequently the only way to obtain approximate results. It is therefore hoped that the gap between these two directions may eventually be diminished. Idealistically, this could be achieved when theoreticians learn about practical problems and practitioners learn about theory. In present times of great specialization, this is highly unrealistic. Nevertheless, one could try to work in this direction, at least with our students in universities, by stressing the importance of theory and applications.