Minimizing Age of Information with Soft Updates

TL;DR

This paper introduces and analyzes a novel 'soft update' model for information freshness, where updates gradually reduce age over time, optimizing update timing and duration under given constraints.

Contribution

It proposes the concept of soft updates with gradual age reduction, deriving optimal update schedules for two decay models, expanding the understanding of age minimization strategies.

Findings

Optimal update start times and durations are derived for both models.

Exponential decay model results in specific scheduling policies.

Linear decay model yields different optimal update strategies.

Abstract

We consider an information updating system where an information provider and an information receiver engage in an update process over time. Different from the existing literature where updates are countable (hard) and take effect either immediately or after a delay, but $instantaneously$ in both cases, here updates start taking effect right away but $gradually$ over time. We coin this setting $soft$ $updates$. When the updating process starts, the age decreases until the soft update period ends. We constrain the number of times the information provider and the information receiver meet (number of update periods) and the total duration of the update periods. We consider two models for the decrease of age during an update period: In the first model, the rate of decrease of age is proportional to the current age, and in the second model, the rate of decrease of age is constant. The first model results in an exponentially decaying age, and the second model results in a linearly decaying age. In both cases, we determine the optimum updating schemes, by determining the optimum start times and optimum durations of the updates, subject to the constraints on the number of update periods and the total update duration.