Performance Analysis of Slotted-Aloha with Mandatory Access and Retries in a Finite Frame

In recent medium access control (MAC) protocols, such as the ones adopted in IEEE 802.11ad and IEEE 802.11ay, stations mandatorily access one of the NS > 0 consecutive slots forming a frame. This can be seen as a variant of the traditional slotted-aloha (SA), where instead of accessing a slot with probability p and not accessing in the finite frame with probability (1-p)NS, a station always accesses at least once in a frame, i.e., stations mandatorily access in a frame's slot. Additionally, a station can also perform multiple retries in the frame when the previous attempt did not succeed. Given the lack of modeling efforts and performance evaluation for SA schemes with mandatory access and retries (SAMAR), in this letter, we evaluate the expected number of stations that can successfully access the channel in a frame composed of a finite number of slots. Contrarily to SA, the analysis of SAMAR performance is challenging due to its enumerative nature. We propose an innovative recursive model of SAMAR performance, showing that SAMAR can achieve higher performance than that of SA parameterized with asymptotically optimal access probabilities. A comparative analysis shows the operational region where SAMAR overpasses SA's performance, which is of crucial importance to define the number of slots of the SAMAR frame.