Minimizing the Age of Missed and False Alarms in Remote Estimation of Markov Sources
Jiping Luo, Νικόλαος Παππάς · 2024
We consider the remote estimation of a discrete-state Markov source with normal and alarm states. Data significance is revealed via two semantic attributes: 1) Erroneously announcing a normal state at the destination when the source is actually in an alarm state (i.e., missed alarm error) incurs a significantly higher cost than falsely announcing an alarm state when the source is in a normal state (i.e., false alarm error). 2) Successive reception of an estimation error may cause significant lasting impact, e.g., maintenance cost and wrong operations. Motivated by this, we assign different costs to different estimation errors and introduce two new age metrics, namely the Age of Missed Alarm (AoMA) and the Age of False Alarm (AoFA), to account for the lasting impact incurred by different estimation errors. We aim to achieve an optimal trade-off between the cost of estimation error, lasting impact, and communication utilization. The problem is formulated as an infinite-state Markov decision process (MDP). We show that the optimal policy exhibits a switching structure, i.e., triggering transmissions only when the AoMA or AoFA exceeds a threshold. Numerical results underscore that our approach significantly reduces the amount of less important information transmitted in the networks.