Delay-Sensitive Energy-Harvesting Wireless Sensors: Optimal Scheduling, Structural Properties, and Approximation Analysis

We consider an energy harvesting sensor transmitting latency-sensitive data over a fading channel. We aim to find the optimal transmission scheduling policy that minimizes the packet queuing delay given the available harvested energy. We formulate the problem as a Markov decision process (MDP) over a state-space spanned by the transmitter's buffer, battery, and channel states, and analyze the structural properties of the resulting optimal value function, which quantifies the long-run performance of the optimal scheduling policy. We show that the optimal value function (i) is non-decreasing and has increasing differences in the queue backlog; (ii) is non-increasing and has increasing differences in the battery state; and (iii) is submodular in the buffer and battery states. Taking advantage of these structural properties, we derive an approximate value iteration algorithm that provides a controllable tradeoff between approximation accuracy, computational complexity, and memory, and we prove that it converges to a near-optimal value function and policy. Our numerical results confirm these properties and demonstrate that the resulting scheduling policies outperform a greedy policy in terms of queuing delay, buffer overflows, energy efficiency, and sensor outages.