On Age of Information for Discrete Time Status Updating System With Ber/G/1/1 Queues

TL;DR

This paper analyzes the stationary age of information distribution in a discrete time Ber/G/1/1 queueing system, deriving formulas and comparing discrete and continuous AoI, demonstrating the applicability of standard queueing theory to discrete AoI analysis.

Contribution

It provides a general formula for the stationary AoI distribution in discrete time queues and shows the effectiveness of standard queueing theory for discrete AoI analysis.

Findings

Derived explicit AoI distribution formulas for Ber/G/1/1 queues.

Compared discrete and continuous AoI, highlighting differences in mean values.

Proved standard queueing theory applies to discrete AoI analysis.

Abstract

In this paper, we consider the age of information (AoI) of a discrete time status updating system, focusing on finding the stationary AoI distribution assuming that the Ber/G/1/1 queue is used. Following the standard queueing theory, we show that by invoking a two-dimensional state vector which tracks the AoI and packet age in system simultaneously, the stationary AoI distribution can be derived by analyzing the steady state of the constituted two-dimensional stochastic process. We give the general formula of the AoI distribution and calculate the explicit expression when the service time is also geometrically distributed. The discrete and continuous AoI are compared, we depict the mean of discrete AoI and that of continuous time AoI for system with M/M/1/1 queue. Although the stationary AoI distribution of some continuous time single-server system has been determined before, in this paper, we shall prove that the standard queueing theory is still appliable to analyze the discrete AoI, which is even stronger than the proposed methods handling the continuous AoI.