This paper presents a first fully analytical approach to performance evaluation of D2D communication systems, which does not assume the system to be in saturated conditions. We adopt a Coupled Processors model to describe a cellular scenario with D2D users sharing radio resources with cellular users, i.e., adopting in-band underlay D2D schemes. We derive sufficient conditions for stability of such system, characterizing the effect of D2D transmissions on cellular user performance. Moreover, we present a computationally feasible method for the determination of a proportionally fair allocation of resources. We show that, in non-saturated networks, such an allocation sensibly improves the one derived under the assumption of saturation. Our results show the importance of accurately modelling the interdependence in users performance in the design and evaluation of a D2D cellular system.