On the Age of Information in Single-Server Queues with Aged Updates

2025-06-24

AI Summary

Conventional Age of Information (AoI) analysis assumes zero initial age for update packets, neglecting non-negligible prior delays—introducing systematic bias in freshness evaluation. Method: We model AoI in a single-server queue with updates possessing non-zero initial age, leveraging queuing theory and stochastic processes to accommodate forwarding, tandem, and retransmission configurations. Contribution/Results: We derive the first general closed-form expression for average AoI incorporating an initial-age correction term; rigorously establish its upper and lower bounds; and prove that, under independent arrivals, the correction term scales linearly with initial age. Experimental validation on multi-stage tandem networks confirms tight bound convergence and demonstrates substantial improvement in AoI estimation accuracy—particularly critical for multi-hop communication and distributed sensing—thereby rectifying the inherent inaccuracy of the zero-initial-age assumption.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Agent Communication
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Social Networks and Social Media: Influence propagation, information diffusion, and the prediction on networks
• Systems and Infrastructure for Web, Mobile and WoT: Web performance, measurement, and characterization
• 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) is a performance metric that quantifies the freshness of data in systems where timely updates are critical. Most state-of-the-art methods typically assume that packets enter the monitored system with zero age, neglecting situations, such as those prevalent in multi-hop networks or distributed sensing, where packets experience prior delays. In this paper, the AoI is investigated when packets have a non-zero initial age. We derive an expression for the average AoI in this setting, showing that it equals the standard AoI plus a correction term involving the correlation between packet age and inter-departure times. When these variables are independent, the expression simplifies to an additive correction equal to the mean initial age. In cases where the dependency structure is unknown, we also establish lower and upper bounds for the correction term. We demonstrate the applicability of our approach across various queueing scenarios, such as forwarding, tandem, and retrial queues. Additionally, we explore the accuracy of the derived bounds on a tandem composed of several queues, a model that has not yet been analytically solved from an age perspective.

Problem

• Analyzing Age of Information with non-zero initial packet age
• Deriving average AoI expression including initial age correction
• Establishing bounds for correction term in unknown dependency cases

Innovation

• Analyzes AoI with non-zero initial packet age
• Derives average AoI with correction term
• Establishes bounds for unknown dependency cases