When to pull data from sensors for minimum Distance-based Age of incorrect Information metric

The age of Information (AoI) has been introduced to capture the notion of freshness in real-time monitoring applications. However, this metric falls short in many scenarios, especially when quantifying the mismatch between the current and the estimated states. To circumvent this issue, in this paper, we adopt the age of incorrect of information metric (AoII) that considers the quantified mismatch between the source and the knowledge at the destination. We consider for that a problem where a central entity pulls the information from remote sources that evolve according to a Markovian Process. It selects at each time slot which sources should send their updates. As the scheduler does not know the real state of the remote sources, it estimates at each time the value of AoII based on the Markovian sources' parameters. Its goal is to keep the time average of AoII function as small as possible. We develop a scheduling scheme based on Whittle's index policy for that purpose. To that extent, we proceed by using the Lagrangian Relaxation Approach and establish that the dual problem has an optimal threshold policy. Building on that, we compute the expressions of Whittle's indices. Finally, we provide some numerical results to highlight the performance of our derived policy compared to the classical AoI metric.