The effect of limiting the number of retransmission trials on the stability of slotted ALOHA systems

We investigate the effect of limiting the number of retransmission trials on the stability of slotted ALOHA systems with no capture effect. Using an argument of the catastrophe theory, we a prove that a slotted ALOHA system is mono-stable, if the number of retransmission trials is limited to, at most, eight. We also show how the bistable region is enlarged, as the number of retransmission trials grows over eight.