# Age and Value of Information: Non-linear Age Case

## TL;DR

This paper introduces new metrics, CoUD and VoIU, to quantify and optimize the freshness and value of information in real-time status update systems with non-linear age dynamics.

## Contribution

It extends the concept of information aging by defining CoUD and VoIU metrics, facilitating the analysis and minimization of information staleness in complex systems.

## Key findings

- CoUD effectively measures the cost of stale information.
- VoIU quantifies the value gained from each update.
- The metrics enable optimization of update policies.

## Abstract

We consider a real-time status update system consisting of a source-destination network. A stochastic process is observed at the source, and samples, so called status updates, are extracted at random time instances, and delivered to the destination. In this paper, we expand the concept of information ageing by introducing the Cost of Update Delay (CoUD) metric to characterize the cost of having stale information at the destination. We introduce the Value of Information of Update (VoIU) metric that captures the reduction of CoUD upon reception of an update. The importance of the VoIU metric lies on its tractability which enables the minimization of the average CoUD.