  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.
