Effects of the Auto-Correlation of Delays on the Age of Information: A Gaussian Process Framework

2025-05-19

AI Summary

In large-scale real-time monitoring systems (e.g., communication networks), end-to-end delay autocorrelation significantly degrades Age of Information (AoI) performance—a critical limitation unaddressed under conventional single-server queueing assumptions. Method: We propose a general modeling framework that represents end-to-end delay as a nonnegative continuous-time virtual delay process, decoupling AoI analysis from restrictive queueing assumptions. For the first time in AoI theory, we employ Gaussian processes to rigorously characterize the impact of delay’s second-order statistics—particularly its autocorrelation structure—on AoI degradation. Contribution/Results: We derive closed-form analytical expressions for the transient AoI distribution and establish strict stochastic order relationships linking delay autocorrelation to AoI performance loss. Both theoretical analysis and numerical experiments confirm that strong delay autocorrelation substantially worsens AoI; we further quantify the sensitivity of AoI distribution and expected value to the delay covariance function. This work establishes a novel paradigm for AoI modeling and optimization in complex, correlated-network environments.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Agent Communication
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

The age of information (AoI) has been studied actively in recent years as a performance measure for systems that require real-time performance, such as remote monitoring systems via communication networks. The theoretical analysis of the AoI is usually formulated based on explicit system modeling, such as a single-server queueing model. However, in general, the behavior of large-scale systems such as communication networks is complex, and it is usually difficult to express the delay using simple queueing models. In this paper, we consider a framework in which the sequence of delays is composed from a non-negative continuous-time stochastic process, called a virtual delay process, as a new modeling approach for the theoretical analysis of the AoI. Under such a framework, we derive an expression for the transient probability distribution of the AoI and further apply the theory of stochastic orders to prove that the high dependence of the sequence of delays leads to the degradation of AoI performance. We further consider a special case in which the sequence of delays is generated from a stationary Gaussian process, and we discuss the sensitivity of the AoI to second-order statistics of the delay process through numerical experiments.

Problem

• Analyzing Age of Information (AoI) under complex delay correlations
• Modeling delays using non-negative continuous-time stochastic processes
• Investigating AoI sensitivity to delay statistics in Gaussian processes

Innovation

• Uses virtual delay process for AoI modeling
• Derives transient AoI probability distribution
• Applies Gaussian process for delay analysis