Age-minimal online policies for energy harvesting sensors with random battery recharges

We consider an energy harvesting sensor that is sending measurement updates regarding some physical phenomenon to a destination. The sensor relies on energy harvested from nature to measure and send its updates, and is equipped with a battery of finite size to collect its harvested energy. The energy harvesting process is Poisson with unit rate, and arrives in amounts that fully recharge the battery. Our setting is online in the sense that the times of energy arrivals are revealed causally to the sensor after the energy is harvested; only the statistics of the arrival process is known a priori. Updates need to be sent in a timely manner to the destination, namely, such that the long term average age of information is minimized over the course of communication. The age of information is defined as the time elapsed since the freshest update has reached the destination. We first show that the optimal scheduling update policy is a renewal policy, and then show that it has a multi threshold structure: the sensor sends an update only if the age of information grows above a certain threshold that depends on the available energy.