# The Cost of Delay in Status Updates and their Value: Non-linear Ageing

arXiv: https://arxiv.org/abs/1812.09320 · HTML: https://mlsanity.com/paper/1812.09320/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Dec 2018.

## Built on by (most cited first, 5 of 5)

- [Version age-based client scheduling policy for federated learning](https://mlsanity.com/paper/2402.05407/) (2024)
- [Value of Information and Timing-aware Scheduling for Federated Learning](https://mlsanity.com/paper/2312.10512/) (2023)
- [To Compute or not to Compute? Adaptive Smart Sensing in Resource-Constrained Edge Computing](https://mlsanity.com/paper/2209.02166/) (2022)
- [SECURA: Sigmoid-Enhanced CUR Decomposition with Uninterrupted Retention and Low-Rank Adaptation in Large Language Models](https://mlsanity.com/paper/2502.18168/) (2025)
- [Chronofy: A Temporal-Logical Decay Architecture for Information Validity in Time-Aware Retrieval-Augmented Generation](https://mlsanity.com/paper/2607.20560/) (2026)

## Abstract (arXiv)

We consider a status update communication system consisting of a source-destination link. A stochastic process is observed at the source, where samples are extracted at random time instances, and delivered to the destination, thus, providing status updates for the source. 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. The CoUD captures the freshness of the information at the destination and can be used to reflect the information structure of the source. Moreover, we introduce the value of information of update (VoIU) metric that captures the reduction of CoUD upon reception of an update. Using the CoUD, its by-product metric called peak cost of update delay (PCoUD), and the VoIU, we evaluate the performance of an M/M/1 system in various settings that consider exact expressions and bounds. Our results indicate that the performance of CoUD differs depending on the cost assigned per time unit, however the optimal policy remains the same for linear ageing and varies for non-linear ageing. When it comes to the VoIU the performance difference appears only when the cost increases non-linearly with time. The study illustrates the importance of the newly introduced variants of age, furthermore supported in the case of VoIU by its tractability.