Age Dispersion and Higher-Order AoI in 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.