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Section: Scientific Foundations

Measurements and Mathematical Modeling

Traffic Modeling

The characterization of Internet traffic has become over the past few years one of the major challenging issues in telecommunications networks. As a matter of fact, understanding the composition and dynamics of Internet traffic is essential for network operators in order to control quality of service and supervise their networks. Since the well-known paper by Leland et al. on the self-similar nature of Ethernet traffic in local area networks, a huge amount of work has been devoted to the characterization of Internet traffic. In particular, a number of different hypotheses on the origins and reasons for the self-similarity of Internet traffic have been explored.

A common approach to describing traffic in a backbone network consists in observing the bit rate process evaluated over fixed length intervals of a few hundreds of milliseconds, say. Long range dependence as well as self-similarity are two basic properties of the bit rate process, which have been observed through measurements in many different situations. Different characterizations of the fractal nature of traffic have been proposed in the literature (see for instance Norros on the monofractal characterization of traffic). An exhaustive account of the fractal characterization of Internet traffic can be found in the book by Park and Willinger. Even though long range dependence and self-similarity properties are very intriguing from a theoretical point of view, their significance in network design has recently been questioned.

While self-similar models introduced so far in the literature aim to describe the overall traffic on a link, it is now usual to distinguish short transfers (referred to as mice) and long transfers (referred to as elephants) [31] . This dichotomy was not totally clear up to the recent past (see, for instance, network measurements from the MCI backbone network). However, the distinction between mice and elephants is becoming more and more evident with the emergence of peer-to-peer (p2p) applications, which give rise to a large amount of traffic on a small number of TCP connections. The above observation leads us to analyze ADSL traffic through a flow based approach intended, in particular, to clarify the mice/elephants dichotomy. The intuitive definition of a mouse is that it has such a small number of packets that TCP hardly leaves the slow start regime. Thus, a mouse is not sensitive to the bandwidth sharing imposed by TCP congestion avoidance. On the other hand, elephants are sufficiently large that one can assume they share bottleneck bandwidth through TCP flow control. As a consequence, mice and elephants have a totally different behavior from a modeling point of view.

We consider that describing statistical properties of Internet traffic at packet level is not appropriate, mainly because of the strong dependence properties noted above. At this time scale, signal processing techniques (wavelets, fractal analysis, ...) can lead to a better description of Internet traffic but do not bring the insights necessary for traffic control. It is widely believed that, at user level, independence properties can be assumed (as for telephone networks), just because users behave quite independently. Unfortunately, there is still no agreed stochastic model of typical user activity. Some models have been proposed, but their number of parameters is too large and most cannot be easily inferred from real measurements. We have chosen to look at the traffic of elephants and mice which defines an intermediate time scale. Some independence properties seem to hold at this level and allow the possibility of Markovian analysis. Note that despite some criticism, Markovian techniques are basically the only tools that can give a sufficiently precise description of the evolution of various stochastic models (average behavior, distribution of the time to overflow buffers, ...).


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