Peer-to-peer (p2p) systems have driven a lot of attention in the past decade as they have become a major source of internet traffic. The amount of data flowing through the p2p network is huge and hence difficult both to comprehend and to control. In this work, we take advantage of a new and rich dataset recording p2p activity at a remarkable scale to give some answers to these difficult problems. After extracting the relevant and measurable properties of the network from the data, we develop two models that aim to make the link between the low-level properties of the network, such as the proportion of free-riders or the distribution of the files among the peers, and its highlevel properties, such as the Quality of Service or the diffusion characteristics, which are the interesting ones. We observe a nice agreement between the high-level properties measured on the real data and on the data simulated by our models, which is encouraging for our models to be used in practice as large-scale prediction tools. Using our models, we make a first prediction and show that it is worth spending efforts to reduce the amount of free-riders to improve the availability of files on the network, but only down to about 65% of free-riders
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