2D-AoI: Age-of-Information of Distributed Sensors for Spatio-Temporal Processes

TL;DR

This paper introduces a two-dimensional Age-of-Information model for distributed sensors capturing spatio-temporal processes, accounting for spatial correlations to better quantify data freshness in sensor networks.

Contribution

It proposes a novel 2D-AoI model that incorporates spatial distance and correlation kernels, extending AoI analysis to multi-sensor, spatially distributed systems.

Findings

Spatial distance adds an offset to AoI with exponential kernels.

Different correlation kernels affect AoI dynamics uniquely.

The model enables evaluation of sensor network topologies and densities.

Abstract

The freshness of sensor data is critical for all types of cyber-physical systems. An established measure for quantifying data freshness is the Age-of-Information (AoI), which has been the subject of extensive research. Recently, there has been increased interest in multi-sensor systems: redundant sensors producing samples of the same physical process, sensors such as cameras producing overlapping views, or distributed sensors producing correlated samples. When the information from a particular sensor is outdated, fresh samples from other correlated sensors can be helpful. To quantify the utility of distant but correlated samples, we put forth a two-dimensional (2D) model of AoI that takes into account the sensor distance in an age-equivalent representation. Since we define 2D-AoI as equivalent to AoI, it can be readily linked to existing AoI research, especially on parallel systems. We consider physical phenomena modeled as spatio-temporal processes and derive the 2D-AoI for different Gaussian correlation kernels. For a basic exponential product kernel, we find that spatial distance causes an additive offset of the AoI, while for other kernels the effects of spatial distance are more complex and vary with time. Using our methodology, we evaluate the 2D-AoI of different spatial topologies and sensor densities.