The Age of Information in a Discrete Time Queue: Stationary Distribution and Non-linear Age Mean Analysis
Abstract
In this work, we investigate information freshness in a status update communication system consisting of a source-destination link. Initially, we study the properties of a sample path of the age of information (AoI) process at the destination. We obtain a general formula of the stationary distribution of the AoI, under the assumption of ergodicity. We relate this result to a discrete time queueing system and provide a general expression of the generating function of AoI in relation with the system time and the peak age of information (PAoI) metric. Furthermore, we consider three different single-server system models and we obtain closed-form expressions of the generating functions and the stationary distributions of the AoI and the PAoI. The first model is a first-come-first-served (FCFS) queue, the second model is a preemptive last-come-first-served (LCFS) queue, and the last model is a bufferless system with packet dropping. We build upon these results to provide a methodology for analyzing general non-linear age functions for this type of systems, using representations of functions as power series.
Keywords
Cite
@article{arxiv.2002.08798,
title = {The Age of Information in a Discrete Time Queue: Stationary Distribution and Non-linear Age Mean Analysis},
author = {Antzela Kosta and Nikolaos Pappas and Anthony Ephremides and Vangelis Angelakis},
journal= {arXiv preprint arXiv:2002.08798},
year = {2020}
}