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

## TL;DR

This paper studies an energy harvesting sensor transmitting updates over an erasure channel, optimizing the timing of updates to minimize the long-term average age of information using renewal and threshold-greedy policies.

## Contribution

It characterizes the optimal update policy structure and derives an analytical expression for the best threshold-greedy policy in an online energy harvesting setting.

## Key findings

- Optimal update times form a renewal process.
- Threshold-greedy policies effectively minimize age.
- Analytical derivation of the optimal threshold.

## Abstract

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