Controlled ALOHA with geometric capture probabilities

An infinite user, slotted ALOHA system operating over a capture channel is studied. In a capture channel, differences in the levels of received power and the times of arrival allow the receiver to successfully receive a packet even when two or more have been transmitted simultaneously. The slotted ALOHA system operating over a capture channel is known to be unstable unless a control policy is used. The authors stabilize the system by using a retransmission control algorithm and derive the throughput as a function of the capture parameter