In 5G wireless networks direct device-to-device communication is expected to play a major role. The network users form a point process on the edges of a spatial graph representing the street system. In the simplest setting, the distribution of these users is Poisson conditioned on the street system. Using methods from percolation theory we provide answers to the following core questions in an asymptotic regime: What is the connection probability of devices as a function of distance? What is the proportion of pairs of connected devices? What is the connection probability as a function of the number of hops?
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This talk is based on joint work with Benedikt Jahnel (WIAS) and Elie Calie (Orange S.A.)