Optimality of myopic scheduling and whittle indexability for energy harvesting sensors

Consider a single-hop wireless sensor network, where a central node (or fusion center, FC) collects data from a set of M energy harvesting (EH)-capable sensors (or nodes). In each time-slot only a subset of K ≤ M nodes can be scheduled by the FC for transmission over K orthogonal communication resources (e.g., frequencies). The scheduling problem is tackled by assuming that the FC has no direct access to the instantaneous states of the nodes´ batteries, but it only knows the outcomes of previous transmissions attempts and the statistical properties of the energy harvesting/discharging processes. Based on a simple Markovian modeling of the EH and battery leakage processes, the FC´s scheduling problem is formulated as partially observable Markov decision processes (POMDPs) and then cast into a restless multi-armed bandit (RMAB) framework. It is shown that in some special cases, a myopic (or greedy) scheduling policy is optimal, and that such a policy coincides with the so called Whittle index policy.