M/D/1/1 loss system with interference and applications to transmit-only sensor networks

We propose and analyze a probabilistic model of packet reception in the steady state regime of a non-slotted wireless communication channel. It is an extension of the classical M/D/1/1 Erlang´s loss model where the interference created by different packet emissions is introduced by means of a shot-noise process. More precisely, we assume that a given packet is admitted by the single receiver if this latter is idle at the packet arrival epoch and successfully received if, in addition, its signal-to-interference-and-noise ratio averaged over the reception period is large enough. As the main result we prove an analog of the Erlang´s formula for the ergodic rate of the successfully received packets. Our work is motivated by some applications to transmit-only sensor networks.