The prudence transmission method II (PTM II): on the maximum and minimum values of retransmission cut-off method for slotted ALOHA

A stable operation of slotted ALOHA can be achieved by reducing the maximum transmission number for a specific limit of the new packet generation rate. We introduced and analysed a transmission method with the retransmission cut-off called the prudence transmission method II (PTM II) to maximise the throughput. Results show that the retransmission cut-off is not needed for a stable operation of slotted ALOHA if the new packet generation rate is less than (1+1/z)(1-1/N)^N-1 packet per time slot with the type I capture, where z, is the capture ratio and N is the number of users. With the type II of capture, this limit can be obtained by putting the capture ratio z equal to one, however the type II capture is conceptually different compared to the type I. The maximum and minimum values of the new packet generation rates with and without capture, and the proper adjustment of maximum allowable number of transmissions for a given new packet generation rate is derived analytically. A stable operating region in terms of the new packet generation rate and the corresponding number of transmissions is also discussed