Using Erasure Feedback for Online Timely Updating with an Energy\n Harvesting Sensor

A real-time status updating system is considered, in which an energy\nharvesting sensor is acquiring measurements regarding some physical phenomenon\nand sending them to a destination through an erasure channel. The setting is\nonline, in which energy arrives in units according to a Poisson process with\nunit rate, with arrival times being revealed causally over time. Energy is\nsaved in a unit-sized battery. The sensor is notified by the destination of\nwhether updates were erased via feedback. Updates need to reach the destination\nsuccessfully in a timely fashion, namely, such that the long term average age\nof information, defined as the time elapsed since the latest successful update\nhas reached the destination, is minimized. First, it is shown that the optimal\nstatus update policy has a renewal structure: successful update times should\nconstitute a renewal process. Then, threshold-greedy policies are investigated:\na new update is transmitted, following a successful one, only if the age of\ninformation grows above a certain threshold; and if it is erased, then all\nsubsequent update attempts are greedily scheduled whenever energy is available.\nThe optimal threshold-greedy policy is then analytically derived.\n