A Worst-Case Approximate Analysis of Peak Age-of-Information Via Robust Queueing Approach

TL;DR

This paper introduces a robust queueing approach to analyze the Peak Age-of-Information (PAoI), providing bounds that are accurate across various traffic conditions, including heavy-tailed and correlated processes, where traditional methods struggle.

Contribution

It develops a new robust queueing framework to approximate PAoI for general arrival and service processes, extending analysis to multi-source systems with coupled uncertainties.

Findings

The derived bounds accurately approximate expected PAoI under diverse traffic conditions.

The approach outperforms traditional probabilistic bounds, especially under light and high load scenarios.

Numerical results validate the effectiveness of the new bounds in practical settings.

Abstract

A new timeliness metric, called Age-of-Information (AoI), has recently attracted a lot of research interests for real-time applications with information updates. It has been extensively studied for various queueing models based on the probabilistic approaches, where the analyses heavily depend on the properties of specific distributions (e.g., the memoryless property of the exponential distribution or the i.i.d. assumption). In this work, we take an alternative new approach, the robust queueing approach, to analyze the Peak Age-of-Information (PAoI). Specifically, we first model the uncertainty in the stochastic arrival and service processes using uncertainty sets. This enables us to approximate the expected PAoI performance for very general arrival and service processes, including those exhibiting heavy-tailed behaviors or correlations, where traditional probabilistic approaches cannot be applied. We then derive a new bound on the PAoI in the single-source single-server setting. Furthermore, we generalize our analysis to two-source single-server systems with symmetric arrivals, which involves new challenges (e.g., the service times of the updates from two sources are coupled in one single uncertainty set). Finally, through numerical experiments, we show that our new bounds provide a good approximation for the expected PAoI. Compared to some well-known bounds in the literature (e.g., one based on Kingman's bound under the i.i.d. assumption) that tends to be inaccurate under light load, our new approximation is accurate under both light and high loads, both of which are critical scenarios for the AoI performance.