Information Aging through Queues: A Mutual Information Perspective

TL;DR

This paper introduces a mutual information-based measure for information freshness, analyzes optimal sampling policies through queue models, and proves that a threshold policy maximizes the expected mutual information over time.

Contribution

It proposes a novel mutual information-based freshness measure and derives the optimal threshold sampling policy for Markov sources in queue systems.

Findings

Optimal sampling policy is a threshold policy.

Exact threshold value for maximizing mutual information.

Numerical results compare different sampling strategies.

Abstract

In this paper, we propose a new measure for the freshness of information, which uses the mutual information between the real-time source value and the delivered samples at the receiver to quantify the freshness of the information contained in the delivered samples. Hence, the "aging" of the received information can be interpreted as a procedure that the above mutual information reduces as the age grows. In addition, we consider a sampling problem, where samples of a Markov source are taken and sent through a queue to the receiver. In order to optimize the freshness of information, we study the optimal sampling policy that maximizes the time-average expected mutual information. We prove that the optimal sampling policy is a threshold policy and find the optimal threshold exactly. Specifically, a new sample is taken once a conditional mutual information term reduces to a threshold, and the threshold is equal to the optimum value of the time-average expected mutual information that is being maximized. Numerical results are provided to compare different sampling policies.