Optimal power and retransmission control policies for random access systems

We consider in this study dynamic control policies for slotted Aloha random access systems. New performance bounds are derived when random access is combined with power control for system optimization, and we establish the existence of optimal control approaches for such systems. We analyze throughput and delay when the number of backlogged users is known, where we can explicitly obtain optimal policies and analyze their corresponding performance using Markov Decision Process (MDP) theory with average cost criterion. For the realistic unknown-backlog case, we establish the existence of optimal backlog-minimizing policies for the same range of arrival rates as the ideal known-backlog case by using the theory of MDPs with Borel state space and unbounded costs. We also propose suboptimal control policies with performance close to the optimal without sacrificing stability. These policies perform substantially better than existing "Certainty Equivalence" controllers.