On Discrete Age of Information of Infinite Size Status Updating System

TL;DR

This paper analyzes the discrete-time status updating system with infinite size, deriving explicit formulas for the average age of information and its stationary distribution, and characterizing the system's AoI dynamics.

Contribution

It provides a complete characterization of AoI in infinite size systems using a two-dimensional state model, including explicit stationary distribution and mean AoI.

Findings

Explicit expression for average AoI derived.

Stationary distribution of AoI obtained.

System's AoI dynamics characterized with a two-dimensional model.

Abstract

In this paper, for the discrete time status updating system with infinite size, we derive the explicit expression of average age of information (AoI), and the AoI's stationary distribution. Based on the discussions of difference between finite and infinite size status updating systems, we successfully characterize the random dynamics of system's AoI using a two-dimensional state vector, which simultaneously tracks the real time AoI and the age of packet currently under service. We constitute the two-dimensional age process and completely solve all the stationary probabilities. Then, as one of the marginal distributions, the stationary distribution of system's AoI is derived, and with which the mean of the AoI is also determined.