Fractal queueing refers to contention models in which traffic processes (e.g., arrivals, service times, buffer occupancy) exhibit fluctuations or variations over a wide range of time scales. In contrast, conventional queueing theory is based on implicit assumptions (e.g., Markov property, exponential distributions) that restrict the fluctuations of the underlying traffic processes to a limited range of time scales. The authors motivate the need for fractal queueing models with traffic measurement studies from a variety of modern communications networks. These studies strongly suggest that actual traffic processes are consistent with ‘fractal’ features (i.e., involving many time scales), such as long-range dependence and the infinite variance phenomenon. The authors then consider the problem of performing queueing analysis on the basis of fractal traffic descriptions, and illustrate how models that parsimoniously capture the empirically observed fractal traffic characteristics give rise to a much richer set of queueing responses than is known for conventional queueing theory. There is considerable scope for future research in the description, analysis, and control of fractal queueing models, and they conclude with a review of open problems.
