On the Stability of Slotted ALOHA Systems

In this correspondence we prove the following properties of the stability of the finite population model of slotted ALOHA systems. 1) The input-output packet flow balance principle [1] and the concept of expected drift [2] used for the stability analysis of the slotted ALOHA system are mathemtaically equivalent. 2) The slotted ALOHA system can only have either one stable equilibrium point or three equilibrium points, with the first one and the third one stable and the second one unstable. 3) If the retransmission probability (which is assumed to be greater than the probability of new packet generation) is less than or equal to
2/N
, where
N
is the total number of active users in the system, then the system has only one stable equilibrium point.