Summary of ‘ Queues with Regular Variation ’ by Qing Deng ( D - 44 )

Queueing theory plays an important role in the design of telecommunication networks. Simple models, like fluid queues or classical single-server queues, can often be used to obtain insightful results, e.g., to predict the global traffic behavior. Traditional queueing models typically assume that the interarrival and service times have finite variance (e.g., exponential or Erlang distribution). As a result, the aggregate traffic that is offered by a collection of sources behaves like white noise. Recently, it has become clear that delay and buffer content distributions in modern communication networks often do not exhibit such a behavior like white noise. Many studies on traffic measurements from a variety of communication networks, have shown a striking difference between actual network traffic and assumptions in traditional theoretical traffic models. That is, actual network traffic is often it self-similar or it long-range dependent in nature. In other words, the traffic looks statistically the same over a wide range of time scales, from milliseconds to minutes and even hours. This conclusion is supported by statistical analysis of numerous high-quality Ethernet and Internet traffic measurements.