Stability of a slotted ALOHA system with capture effect

The stability of a slotted ALOHA system with capture effect is investigated under a general communication environment where terminals are divided into two groups (low-power and high-power) and the capture effect is modeled by capture probabilities. An approximate analysis is developed using catastrophe theory in which the effects of system and user parameters on the stability are characterized by the cusp catastrophe. In particular, the authors focus on the low-power group, since it must bear the strain under the capture effect. The stability conditions of the two groups are given explicitly by bifurcation sets