Age of Information for Discrete Time Queues

TL;DR

This paper analyzes the age of information in discrete time queueing systems, deriving explicit formulas for peak and average age across various queue types, and introduces new analytical techniques.

Contribution

It provides the first explicit age expressions for discrete time queues like Ber/G/1 and G/G/∞, and develops novel proof techniques for age analysis.

Findings

Derived explicit peak and average age formulas for Ber/G/1 queues.

Extended age analysis to LCFS and G/G/∞ queues.

Introduced new analytical techniques for discrete time queue age analysis.

Abstract

Age of information (AoI) is a time-evolving measure of information freshness, that tracks the time since the last received fresh update was generated. Analyzing peak and average AoI, two time average metrics of AoI, for various continuous time queueing systems has received considerable attention. We analyze peak and average age for various discrete time queueing systems. We first consider first come first serve (FCFS) Ber/G/1 and Ber/G/1 queue with vacations, and derive explicit expressions for peak and average age. We also obtain age expressions for the last come first serve (LCFS) queue and the $G/G/\infty$ queue. We build upon proof techniques from earlier results, and also present new techniques that might be of independent interest in analyzing age in discrete time queuing systems.