Maximum Asymptotic Stable Throughput of Opportunistic Slotted ALOHA and Applications to CDMA Networks

In this paper we study the maximum asymptotic stable throughput of an opportunistic slotted ALOHA protocol. We provide a characterization of the maximum stable throughput as the number of users in the system goes to infinity. We then apply our findings to CDMA networks with the signal-to-interference-ratio (SIR) threshold model. It is shown that the slotted ALOHA protocol with the power/transmission control rule that equalizes the reception powers achieves 1 - O(logN/radicN) channel utilization, which is defined as the throughput divided by the optimal throughput N achieved by scheduling. This implies that the slotted ALOHA is asymptotically optimal in the sense that its channel utilization converges to 1 as the spreading gain goes to infinity