Age Minimization with Energy and Distortion Constraints

TL;DR

This paper develops optimal policies for a sensor fusion system to minimize average age of information while satisfying energy and age-dependent distortion constraints, revealing key tradeoffs.

Contribution

It introduces a mixture of threshold-based policies optimized for age, energy, and distortion tradeoffs, with analytical solutions and insights for practical scenarios.

Findings

Optimal policy is a mixture of two threshold-based policies.

Derived analytical average age-cost function and performance in large threshold regime.

Closed-form solution for age-independent distortion constraint case.

Abstract

In this paper, we consider a status update system, where an access point collects measurements from multiple sensors that monitor a common physical process, fuses them, and transmits the aggregated sample to the destination over an erasure channel. Under a typical information fusion scheme, the distortion of the fused sample is inversely proportional to the number of measurements received. Our goal is to minimize the long-term average age while satisfying the average energy and general age-based distortion requirements. Specifically, we focus on the setting in which the distortion requirement is stricter when the age of the update is older. We show that the optimal policy is a mixture of two stationary, deterministic, threshold-based policies, each of which is optimal for a parameterized problem that aims to minimize the weighted sum of the age and energy under the distortion constraint. We then derive analytically the associated optimal average age-cost function and characterize its performance in the large threshold regime, the results of which shed critical insights on the tradeoff among age, energy, and the distortion of the samples. We have also developed a closed-form solution for the special case when the distortion requirement is independent of the age, arguably the most important setting for practical applications.