Performance analysis for a stabilized multi-channel slotted ALOHA algorithm

We study the slotted ALOHA with multiple random access channels, the so called multi-channel ALOHA (MC-ALOHA). It is well known that single-channel ALOHA (SC-ALOHA) is unstable. Not surprisingly, MC ALOHA is also unstable. A stabilization algorithm for MC-ALOHA has been proposed in [D. Shen and V.O.K. Li, 2002], in which the pseudo-Bayesian algorithm in SC-ALOHA was extended to achieve stabilized MC-ALOHA. The idea is to estimate the number of attempting users so that user transmission probability can be adjusted accordingly. In this paper, we give a theoretical analysis on the algorithm performance for cases with limited and unlimited number of users by assuming perfect estimate. The theoretical results are validated by simulation, which shows the stabilization algorithm performs close to a system with perfect estimate. The simulation results also show that the performance of the stabilized algorithm is much better than the non-stabilized algorithm. With the stabilized algorithm, the system is always stable when the new packet arrival rate is less than system capacity. Even when the arrival rate is higher than capacity, system throughput can still be guaranteed.