On the complexity of Internet traffic dynamics on its topology

Most studies of Internet traffic rely on observations from a single link. The corresponding traffic dynamics has been studied for more than a decade and is well understood. The study of how traffic on the Internet topology, on the other hand, is poorly understood and has been largely limited to the distribution of traffic among source-destination pairs inside the studied network, also called the traffic matrix. In this paper, we make a first step towards understanding the way traffic gets distributed onto the whole topology of the Internet. For this, we rely on the traffic seen by a transit network, for a period of more than a week. As we are still at the stage of understanding the topological traffic distribution, we do not try to model the traffic dynamics. Rather we concentrate on understanding the complexity of describing the traffic observed by a transit network, how it maps onto the AS-level topology of the Internet and how it changes over time. For this, we rely on well-known tools of multi-variate analysis and multi-resolution analysis. Our first observation is that the structure of the Internet topology highly impacts the traffic distribution. Second, our attempts at compressing the traffic on the topology through dimension reduction suggests two options for traffic modeling: (1) to ignore links on the topology for which we do not see much traffic, or (2) to ignore time scales smaller than a few hours. In either case, important properties of the traffic might be lost, so might not be an option to build realistic models of Internet traffic. Realistic models of Internet traffic on the topology are not out of reach though. In this paper, we identify two properties such models should have: (1) use a compact representation of the dependencies of the traffic on the topology, and (2) be able to capture the complex multi-scale nature of traffic dynamics on different types of links.