is given by: and its cumulative distribution function is given by: where k represents the smallest value the random variable can take. Readers interested in a more rigorous mathematical treatment of the subject are referred to the external links section. What causes long-tail traffic? In general, there are three main theories for the causes of long-tail traffic (see a review of all three causes). First, is a cause based in the application layer which theorizes that user session durations vary with a long-tail distribution due to the file size distribution. If the distribution of file sizes is heavy-tailed then the superposition of many file transfers in a client/server network environment will be long-range dependent. Additionally, this causal mechanism is robust with respect to changes in network resources (bandwidth and buffer capacity) and network topology. This is currently the most popular explanation in the engineering literature and the one with the most empirical evidence through observed file size distributions. Second, is a transport layer cause which theorizes that the feedback between multiple TCP streams due to TCP's congestion avoidance algorithm in moderate to high packet loss situations causes self-similar traffic or at least allows it to propagate. However, this is believed only to be a significant factor at relatively short timescales and not the long-term cause of self-similar traffic. Finally, is a theorized link layer cause which is predicated based on physics simulations of packet switching networks on simulated topologies. At a critical packet creation rate, the flow in a network becomes congested and exhibits 1/f noise and long-tail traffic characteristics. There have been criticisms on these sorts of models though as being unrealistic in that network traffic is long-tailed even in non-congested regions and at all levels of traffic. Simulation showed that long-range dependence could arise in the queue length dynamics at a given node (an entity which transfers traffic) within a communications network even when the traffic sources are free of long-range dependence. The mechanism for this is believed to relate to feedback from routing effects in the simulation. Modelling long-tail traffic Modelling of long-tail traffic is necessary so that networks can be provisioned based on accurate assumptions of the traffic that they carry. The dimensioning and provisioning of networks that carry long-tail traffic is discussed in the next section. Since (unlike traditional telephony traffic) packetised traffic exhibits self-similar or fractal characteristics, conventional traffic models do not apply to