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.