Distribution of the Number of Users per Base Station in Cellular Networks

We consider the number of users associating with each base station in a cellular network. Extending and unifying the characterizations for certain settings available in the literature, we derive a result that is asymptotic in the strength of the shadowing, yet otherwise universally valid: it holds for every network geometry and shadowing distribution. We then illustrate how this result provides excellent representations in various classes of networks and with realistic shadowing strengths, evidencing broad applicability.