# Optimal Status Updating with a Finite-Battery Energy Harvesting Source

## TL;DR

This paper analyzes optimal update policies for energy-harvesting sensors with finite batteries, proving that threshold-based policies are optimal and showing that increasing battery size significantly reduces age penalty, especially at small capacities.

## Contribution

It establishes the structural optimality of monotone threshold policies for finite-battery energy harvesting sources and develops an algorithm to compute these thresholds.

## Key findings

- Optimal policies are monotone threshold policies based on battery level and age.
- Increasing battery capacity notably reduces age penalty, especially from one to two units of energy.
- Over half of the potential age reduction occurs when increasing battery size from one to two.

## Abstract

We consider an energy harvesting source equipped with a finite battery, which needs to send timely status updates to a remote destination. The timeliness of status updates is measured by a non-decreasing penalty function of the Age of Information (AoI). The problem is to find a policy for generating updates that achieves the lowest possible time-average expected age penalty among all online policies. We prove that one optimal solution of this problem is a monotone threshold policy, which satisfies (i) each new update is sent out only when the age is higher than a threshold and (ii) the threshold is a non-increasing function of the instantaneous battery level. Let $\tau_B$ denote the optimal threshold corresponding to the full battery level $B$, and $p(\cdot)$ denote the age-penalty function, then we can show that $p(\tau_B)$ is equal to the optimum objective value, i.e., the minimum achievable time-average expected age penalty. These structural properties are used to develop an algorithm to compute the optimal thresholds. Our numerical analysis indicates that the improvement in average age with added battery capacity is largest at small battery sizes; specifically, more than half the total possible reduction in age is attained when battery storage increases from one transmission's worth of energy to two. This encourages further study of status update policies for sensors with small battery storage.