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

TL;DR

This paper develops an optimal transmission policy for a source communicating with two gossiping receivers, balancing AoI and transmission costs using an MDP framework, and reveals structural properties of the optimal policy.

Contribution

It formulates a joint AoI and cost optimization problem for gossiping networks and characterizes the optimal policy's threshold structure using RVI, a novel approach in this context.

Findings

Optimal policy has an age-difference threshold structure.

Direct transmission is optimal when minimum AoI is high and age difference is small.

Gossiping can reduce transmission costs effectively.

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.