Diffusion limit of a modified Erlang-B system with sensing time of secondary users

We analyze a queueing model for cognitive wireless networks using the asymptotic-diffusion method (Moiseev et al. (2020); Nazarov et al. (2020)). Cognitive wireless is a technology that resolves radio spectrum shortages by allowing secondary users (SUs, unlicensed users) to occupy channels initially assigned to primary users (PUs, licensed users). SUs need to sense the channel availability upon arrival. After sensing, an SU can transmit if there is an idle channel; otherwise, the SU must continue sensing. We consider the situation where SUs may be interrupted by the arrivals of PUs when all channels are occupied. We derive a diffusion limit for the queueing model when the SUs' mean sensing time tends to infinity. The diffusion limit leads to an approximate probability distribution of the number of sensing SUs. Finally, we derive a necessary stability condition which turns out to be consistent with the sufficient condition obtained in previous research.