Delay Analysis of Slotted ALOHA in Capture Channels for the Two User Case

We consider the effect of capture on delay in buffered slotted ALOHA based random access systems for the two user case. In a capture channel, at most one user can have a successful packet transmission when both users transmit. For symmetric Bernoulli arrival rates and a symmetric capture model, we characterize the average delay in terms of the retransmission probability and the capture model parameters. Further, we provide exact expressions for the delay minimizing retransmission probability for all possible capture models. We find that as soon as there is a nonzero capture probability, there is a non-empty subset of ALOHA stabilizable rates for which the optimal retransmission probability is one. We also find that when the capture probability crosses a threshold, the optimal retransmission probability is one for all stabilizable rates.