Joint performance analysis of ages of information in a multi-source pushout server

TL;DR

This paper develops a framework to analyze the joint behavior of multiple Age of Information metrics in multi-source systems, providing new insights into their correlation and performance.

Contribution

It introduces a novel framework for joint AoI analysis in multi-source systems and derives a closed-form formula for the joint Laplace transform in a pushout server.

Findings

Derived a closed-form formula for joint AoI Laplace transform

Analyzed correlation properties of AoIs in two-source systems

Provided insights into AoI correlation in shared resource systems

Abstract

Age of information (AoI) has been widely accepted as a measure quantifying freshness of status information in real-time status update systems. In many of such systems, multiple sources share a limited network resource and therefore the AoIs defined for the individual sources should be correlated with each other. However, there are not found any results studying the correlation of two or more AoIs in a status update system with multiple sources. In this work, we consider a multi-source system sharing a common service facility and provide a framework to investigate joint performance of the multiple AoIs. We then apply our framework to a simple pushout server with multiple sources and derive a closed-form formula of the joint Laplace transform of the AoIs in the case with independent M/G inputs. We further show some properties of the correlation coefficient of AoIs in the two-source system.