Age-Minimal Online Policies for Energy Harvesting Sensors with\n Incremental Battery Recharges

A sensor node that is sending measurement updates regarding some physical\nphenomenon to a destination is considered. The sensor relies on energy\nharvested from nature to transmit its updates, and is equipped with a finite\n$B$-sized battery to save its harvested energy. Energy recharges the battery\nincrementally in units, according to a Poisson process, and one update consumes\none energy unit to reach the destination. The setting is online, where the\nenergy arrival times are revealed causally after the energy is harvested. The\ngoal is to update the destination in a timely manner, namely, such that the\nlong term average age of information is minimized, subject to energy causality\nconstraints. The age of information at a given time is defined as the time\nspent since the latest update has reached the destination. It is shown that the\noptimal update policy follows a renewal structure, where the inter-update times\nare independent, and the time durations between any two consecutive events of\nsubmitting an update and having $k$ units of energy remaining in the battery\nare independent and identically distributed for a given $k\\leq B-1$. The\noptimal renewal policy for the case of $B=2$ energy units is explicitly\ncharacterized, and it is shown that it has an energy-dependent threshold\nstructure, where the sensor updates only if the age grows above a certain\nthreshold that is a function of the amount of energy in its battery.\n