Age of Information Versions: A Semantic View of Markov Source Monitoring

We consider the problem of real-time remote monitoring of a two-state Markov process, where a sensor observes the source state and decides whether to transmit updates over an unreliable channel. We introduce a change-aware randomized stationary policy, in which the source is sampled probabilistically whenever its state changes, and a semantics-aware randomized stationary policy, in which sampling is performed probabilistically based on the current source state and whether the system was in sync in the previous time slot. We then propose two new performance metrics:the Version Innovation Age (VIA), which measures significant changes in content between versions, andthe Age of Incorrect Version (AoIV), which quantifies the outdated versions at the receiver compared to the source when the system is in an incorrect state. We analyze their performance under the proposed and other state-of-the-art sampling policies. Specifically, we derive closed-form expressions for the distributions and averages of VIA, AoIV, and the Age of Incorrect Information (AoII), and formulate three constrained optimization problems to minimize them while accounting for constraints on the time-averaged sampling cost and the reconstruction error. Finally, we compare various sampling and transmission policies and identify the conditions under which each policy performs best.