Optimal Scheduling over Time-Varying Channels with Traffic Admission Control: Structural Results and Online Learning Algorithms

This work studies the joint scheduling- admission control (SAC) problem for a single user over a fading channel. Specifically, the SAC problem is formulated as a constrained Markov decision process (MDP) to maximize a utility defined as a function of the throughput and queue size. The optimal throughput- queue size trade-off is investigated. Optimal policies and their structural properties (i.e., monotonicity and convexity) are derived for two models: simultaneous and sequential scheduling and admission control actions. Furthermore, we propose online learning algorithms for the optimal policies for the two models when the statistical knowledge of the time-varying traffic arrival and channel processes is unknown. The analysis and algorithm development are relied on the reformulation of the Bellman´s optimality equations using suitably defined state-value functions which can be learned online, at transmission time, using time-averaging. The learning algorithms require less complexity and converge faster than the conventional Q-learning algorithms. This work also builds a connection between the MDP based formulation and the Lyapunov optimization based formulation for the SAC problem. Illustrative results demonstrate the performance of the proposed algorithms in various settings.