Mathematics in Internet Traffic Data Analysis
The Internet traffic data have been found to possess extreme variability and bursty structures in a wide range of time-scales, so that there is no definite duration of busy or silent periods. But there is a self-similarity for which it is possible to characterize the data. The self-similar nature was first proposed by Leland et a1 and subsequently established by others in a flood of research works. It was then a new concept against the long believed idea of Poisson traffic. The traditional Poison model, a short ranged process, assumed the variation of data flow to be finite but the observations on Internet traffic proved otherwise.