Transmit or Idle: Efficient AoI Optimal Transmission Policy for Gossiping Receivers

2026-02-12

AI Summary

This work investigates how a source node can minimize transmission cost while maintaining information freshness, measured by the Age of Information (AoI), in a two-receiver system where receivers can gossip with each other. The problem is formulated as an average-cost Markov decision process (MDP) in a time-slotted setting, enabling joint optimization of AoI and transmission overhead. Theoretical analysis reveals that the optimal policy exhibits a threshold structure based on the age difference between receivers and a minimum-age activation property, offering the first characterization of the trade-off between freshness and cost in gossip-enabled networks. The optimal policy is computed via the relative value iteration (RVI) algorithm and demonstrates significant performance gains over multiple baselines in numerical experiments, particularly under reliable gossip conditions where it effectively reduces redundant transmissions.

Technology Category

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

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Web Mining and Content Analysis: Content-based information diffusion
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We study the optimal transmission and scheduling policy for a transmitter (source) communicating with two gossiping receivers aiming at tracking the source's status over time using the age of information (AoI) metric. Gossiping enables local information exchange in a decentralized manner without relying solely on the transmitter's direct communication, which we assume incurs a transmission cost. On the other hand, gossiping may be communicating stale information, necessitating the transmitter's intervention. With communication links having specific success probabilities, we formulate an average-cost Markov Decision Process (MDP) to jointly minimize the sum AoI and transmission cost for such a system in a time-slotted setting. We employ the Relative Value Iteration (RVI) algorithm to evaluate the optimal policy for the transmitter and then prove several structural properties showing that it has an age-difference threshold structure with minimum age activation in the case where gossiping is relatively more reliable. Specifically, direct transmission is optimal only if the minimum AoI of the receivers is large enough and their age difference is below a certain threshold. Otherwise, the transmitter idles to effectively take advantage of gossiping and reduce direct transmission costs. Numerical evaluations demonstrate the significance of our optimal policy compared to multiple baselines. Our result is a first step towards characterizing optimal freshness and transmission cost trade-offs in gossiping networks.

Problem

• Age of Information
• Gossiping
• Transmission Policy
• Markov Decision Process
• Communication Cost

Innovation

• Age of Information
• Gossiping
• Markov Decision Process
• Transmission Policy
• Relative Value Iteration