Traffic Self-Similarity

Statistical analysis of high-resolution traffic measurements from a wide range of working packet networks (e.g., Ethernet LANs, WANs, CCSN/SS7, ISDN and VBR video over ATM) have convincingly shown the presence of fractal or self-similar properties in both local area and wide area traffic traces [2, 3, 5, 15, 19]. That means that similar statistical patterns may occur over different time scales that can vary by many orders of magnitude (i.e., ranging from milliseconds to minutes and even hours). This discovery calls to question some of the basic assumptions made by earlier research done in control, engineering, and operations of broadband integrated systems. The fact that network traffic is inherently fractal or long-range dependent (LRD) and many studies assume traffic to be short-range dependent (SRD) leads one to question the extent to which the results of these studies are applicable in practice. At the time being, there is mounting evidence that LRD is of fundamental importance for a number of teletraffic engineering problems, such as traffic measurements [24], queueing behaviour and buffer sizing [6, 16], admission control [4] and congestion control [21]. Unlike traditional packet traffic models, which give rise to exponential tail behavior in queue size distributions and typically result in overly optimistic performance predictions and inadequate resource allocations, fractal traffic models predict hyperbolic or Weibull (stretched exponential) queue size distributions and could therefore affect control and management of present and future packet networks within an integrated framework of end-to-end Quality of Service (QoS) provision. This also indicates that increasing link capacity could be more effective in improving performance than increasing buffer size. Although similar processes have been observed and analysed in a number of other areas like, for instance, hydrology, biophysics, financial economics [23], the work on fractal dynamics of network traffic behaviour is relatively new. While most of the work done in science and engineering has almost exclusively focused on statistical and practical features of fractal models (e.g., data analysis, mathematical modeling), the engineering impacts on performance and analysis have not yet received an adequate interest. This is mainly because of the difficulties related to analysis and the ability to use these models in control. Self-similarity implies that a specific correlation structure is retained over a wide range of time scales, albeit it may come in different forms. In order to be able to do control on such processes, one needs first to explain and to validate on physical grounds the causal mechanisms that could be responsible for generating self-similarity in a realistic network environment. Furthermore, understanding the impacts of such processes is at least as important as the understanding of their physical origins.