Age minimization in energy harvesting communications: Energy-controlled delays

We consider an energy harvesting source that is collecting measurements from a physical phenomenon and sending updates to a destination within a communication session time. Updates incur transmission delays that are function of the energy used in their transmission. The more transmission energy used per update, the faster it reaches the destination. The goal is to transmit updates in a timely manner, namely, such that the total age of information is minimized by the end of the communication session, subject to energy causality constraints. We consider two variations of this problem. In the first setting, the source controls the number of measurement updates, their transmission times, and the amounts of energy used in their transmission (which govern their delays, or service times, incurred). In the second setting, measurement updates externally arrive over time, and therefore the number of updates becomes fixed, at the expense of adding data causality constraints to the problem. We characterize age-minimal policies in the two settings, and discuss the relationship of the age of information metric to other metrics used in the energy harvesting literature.