  We propose a new model for peer-to-peer networking which takes the network
bottlenecks into account beyond the access. This model allows one to cope with
key features of P2P networking like degree or locality constraints or the fact
that distant peers often have a smaller rate than nearby peers. We show that
the spatial point process describing peers in their steady state then exhibits
an interesting repulsion phenomenon. We analyze two asymptotic regimes of the
peer-to-peer network: the fluid regime and the hard--core regime. We get closed
form expressions for the mean (and in some cases the law) of the peer latency
and the download rate obtained by a peer as well as for the spatial density of
peers in the steady state of each regime, as well as an accurate approximation
that holds for all regimes. The analytical results are based on a mix of
mathematical analysis and dimensional analysis and have important design
implications. The first of them is the existence of a setting where the
equilibrium mean latency is a decreasing function of the load, a phenomenon
that we call super-scalability.
