  User distribution in ultra-dense networks (UDNs) plays a crucial role in
affecting the performance of UDNs due to the essential coupling between the
traffic and the service provided by the networks. Existing studies are mostly
based on the assumption that users are uniformly distributed in space. The
non-uniform user distribution has not been widely considered despite that it is
much closer to the real scenario. In this paper, Radiation and Absorbing model
(R&A model) is first adopted to analyze the impact of the non-uniformly
distributed users on the performance of 5G UDNs. Based on the R&A model and
queueing network theory, the stationary user density in each hot area is
investigated. Furthermore, the coverage probability, network throughput and
energy efficiency are derived based on the proposed theoretical model. Compared
with the uniformly distributed assumption, it is shown that non-uniform user
distribution has a significant impact on the performance of UDNs.
