The effect of capture on collision-resolution algorithms

The effect of capture on basic tree collision-resolution algorithms (CRA) in a slotted ALOHA-type broadcasting network is investigated. Two models are described: the general model for which the extended tree algorithms are described; and the simplified model which is used in the analysis part. The application of the basic tree CRA to the situations where the receiver distinguishes between success slots and capture slots and to the one where it cannot is considered. In each case, explicit recursive equations for the simplified model are given, from which the average collision-resolution interval lengths, as well as the maximal throughput are obtained. It is shown that in the presence of capture, the performance of the network improves and the maximal throughput increases. Extensions of the simplified model such as dividing the nodes of the network into K groups instead of two, or considering the situation where capture depends on relative distances and transmission powers, are also discussed. Simulation results are given for the latter situation.