Age of Incorrect Information for Remote Estimation of a Binary Markov Source
Clement Kam, Sastry Kompella, Anthony Ephremides
Abstract
For monitoring applications, the Age of Information (AoI) metric has been the primary focus of recent research, but closely related to monitoring is the problem of real-time or remote estimation. Age of Information has been shown to be insufficient for minimizing remote estimation error, but recently a metric known as Age of Incorrect Information (AoII) was proposed that characterizes the cost of a monitor being in an erroneous state over time. In this work, we study the AoII metric in the simple context of monitoring a symmetric binary information source over a delay system with feedback. We compare three different performance metrics: real-time error, AoI, and AoII. For each metric, we formulate the optimal sampling problem as a Markov decision process and apply a dynamic programming algorithm to compute the optimal performance and policy. We also simulate the system for two sampling policies: sample-at-change and zero-wait, and we observe which policy coincides with the optimal policy for each metric. For a variety of delay distributions and AoII penalty functions, we observe that the optimal policy for the real-time error and for AoII are equal to the sample-at-change policy, whereas the optimal policy for AoI is a threshold policy.