  We develop a flexible and accurate framework for device-to-device (D2D)
communication in the context of a conventional cellular network, which allows
for time-frequency resources to be either shared or orthogonally partitioned
between the two networks. Using stochastic geometry, we provide accurate
expressions for SINR distributions and average rates, under an assumption of
interference randomization via time and/or frequency hopping, for both
dedicated and shared spectrum approaches. We obtain analytical results in
closed or semi-closed form in high SNR regime, that allow us to easily explore
the impact of key parameters (e.g., the load and hopping probabilities) on the
network performance. In particular, unlike other models, the expressions we
obtain are tractable, i.e., they can be efficiently optimized without extensive
simulation. Using these, we optimize the hopping probabilities for the D2D
links, i.e., how often they should request a time or frequency slot. This can
be viewed as an optimized lower bound to other more sophisticated scheduling
schemes. We also investigate the optimal resource partitions between D2D and
cellular networks when they use orthogonal resources.
