Age of Information in Time-Varying Multi-Priority Queues

2026-05-25

AI Summary

This study addresses the challenge of ensuring information freshness in intermittently connected networks, where time-varying arrivals, service interruptions, and interactions among multi-priority traffic severely degrade performance. The authors investigate a single-server queue with multiple priority classes under time-varying arrival and service rates, and for the first time establish that the first-order moment of a specific system state admits an exact closure. This enables the formulation of a finite-dimensional linear time-periodic ordinary differential equation system to characterize the average Age of Information (AoI) and Peak AoI (PAoI) for each priority class. A fixed-point iteration algorithm based on single-period state mapping is further proposed, which is rigorously shown to converge to a unique periodic steady state. Numerical results demonstrate that high-priority traffic significantly reshapes the service dynamics of lower-priority flows, thereby validating both model accuracy and algorithmic efficacy.

Abstract

In networks with intermittent connectivity, such as mobile, aerial, and space systems, maintaining information freshness is complicated by time-varying arrivals, service disruptions, and interactions among traffic classes with different priorities. To capture these effects, we study a multi-priority single-server queue with time-varying arrivals and service rates under intermittent connectivity. Our main result shows that an appropriately selected collection of state-conditioned first moments closes exactly, leading to a finite-dimensional linear time-periodic Ordinary Differential Equation (ODE) system for the mean Age of Information (AoI) and mean Peak Age of Information (PAoI) of each priority class. For periodic arrival and service rates, we define a one-period state map by propagating the ODE over a single period, and use the periodicity condition to formulate the periodic steady state as a fixed point of this map. We then propose a fixed-point iteration algorithm and prove its convergence to the unique periodic steady state (PSS). Numerical results reveal that high-priority traffic can strongly reshape the service process seen by lower-priority classes.

Problem

• Age of Information
• time-varying queues
• multi-priority traffic
• intermittent connectivity
• information freshness

Innovation

• Age of Information
• multi-priority queues
• time-varying systems
• periodic steady state
• fixed-point iteration