The average CRI-length of a controlled ALOHA collision resolution algorithm (Q1208718)

The paper investigates some properties of a hybrid conflict resolution algorithm proposed for a network with a controlled ALOHA protocol. The algorithm adjusts the retransmission probability to the number of colliding stations. It consists of two steps, namely, the estimation of the number \(n\) of collisions and the collision resolution phase, being the ordinary S-ALOHA algorithm which the retransmission probability \(p=1/n\) and delayed transmissions of newly generated packets. The author estimates the number of collisions and gives the average conditional length of CRI for a given number \(n\) of colliding stations. Next, using the Mellin transform technique he proposes an asymptotic analysis of the average value of CRI. The author proves that the average CRI length is of order \(O(n\log n)\) as \(n\) tends to infinity. This result gives some insight to the instability of the described controlled ALOHA algorithm, namely, it shows that even controlling the retransmission probability is not sufficient to guarantee the stability of the considered protocol.