  An important enabler towards the successful deployment of any new
element/feature to the cellular network is the investigation and
characterization of the operational conditions where its introduction will
enhance performance. Even though there has been significant research activity
on the potential of device-to-device (D2D) communications, there are currently
no clear indications of whether D2D communications are actually able to provide
benefits for a wide range of operational conditions, thus justifying their
introduction to the system. This paper attempts to fill this gap by taking a
stochastic geometry approach on characterizing the set (region) of operational
conditions for which D2D communications enhance performance in terms of average
user rate. For the practically interesting case of a heavy loaded network, the
operational region is provided in closed form as a function of a variety of
parameters such as maximum D2D link distances and user densities, reflecting a
wide range of operational conditions (points). It is shown that under the
appropriate deployment scheme, D2D communications can indeed be beneficial not
only for the usually considered regime of "proximal communications" but to a
wide range of operational conditions that include D2D link distances comparable
to the distance to the cellular access point and considerably large user
densities.
