Age Dispersion and Higher-Order AoI in Status Update Systems

2026-08-02

AI Summary

This study addresses the lack of timeliness consistency in status update systems by introducing “age dispersion” as a novel metric, defined as the difference in age between the two most recently received updates, and generalizing it to a k-th order form. Leveraging an M/G/1/1 queueing model, the authors employ stochastic process analysis and mathematical modeling to establish, for the first time, an intrinsic relationship between age dispersion and k-th order Age of Information (AoI). The work not only characterizes the statistical properties of age dispersion but also expands the dimensional framework for evaluating information timeliness, thereby offering new theoretical foundations and optimization criteria for the design of status update systems.

Abstract

We introduce and characterize \emph{age dispersion} as a measure of temporal consistency in status update systems. Age dispersion is defined as the difference between the ages of the two most recently received updates, and its higher-order extension, the {$k$-th} order age dispersion, captures the difference between the ages of the most recent update and the $(k+1)$-th most recent one. We analyze age dispersion in an M/G/1/1 queueing system. Furthermore, we establish connections between the {$k$-th} order age dispersion and the {$k$-th} order age of information (AoI), where the latter quantifies the age of the {$k$-th} most recently received update.

Problem

• age dispersion
• status update systems
• temporal consistency
• higher-order AoI
• age of information

Innovation

• age dispersion
• higher-order AoI
• status update systems
• temporal consistency
• M/G/1/1 queue