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The age of Information (AoI) has been introduced to capture the notion offreshness in real-time monitoring applications. However, this metric fallsshort in many scenarios, especially when quantifying the mismatch between thecurrent and the estimated states. To circumvent this issue, in this paper, weadopt the age of incorrect information metric (AoII) that considers thequantified mismatch between the source and the knowledge at the destinationwhile tracking the impact of freshness. We consider for that a problem where acentral entity pulls the information from remote sources that evolve accordingto a Markovian Process. It selects at each time slot which sources should sendtheir updates. As the scheduler does not know the actual state of the remotesources, it estimates at each time the value of AoII based on the Markoviansources' parameters. Its goal is to keep the time average of the AoII functionas small as possible. For that purpose, We develop a scheduling scheme based onWhittle's index policy. To that extent, we use the Lagrangian RelaxationApproach and establish that the dual problem has an optimal threshold policy.Building on that, we compute the expressions of Whittle's indices. Finally, weprovide some numerical results to highlight the performance of our derivedpolicy compared to the classical AoI metric.

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