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Measurements from an Internet backbone link carrying TCP traffic towards different ADSL areas are analyzed. For traffic analysis, we adopt a flow based approach and the popular mice/elephants dichotomy, where mice refer to short traffic transfers and elephants to long transfers. The originality of the reported experimental data, when compared with previous measurements from very high speed backbone links, is that the commercial traffic includes a significant part generated by peer-to-peer applications. This kind of traffic exhibits some remarkable properties in terms of mice and elephants, as we describe. It turns out that by adopting a suitable level of aggregation, the bit rate of mice can be described by means of a Gaussian process. The bit rate of elephants is smoother than that of mice and can also be well approximated by a Gaussian process.