Version innovation age and age of incorrect version for monitoring Markovian sources

In this paper, we propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) for real-time monitoring of a two-state Markov process over an unreliable channel. We analyze their performance under the change-aware, semantics-aware, and randomized stationary sampling and transmission policies. We derive closed-form expressions for the distribution and the average of VIA, AoIV, and AoII for these policies. We then formulate and solve an optimization problem to minimize the average VIA, subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. Finally, we compare the performance of various sampling and transmission policies and identify the conditions under which each policy outperforms the others in optimizing the proposed metrics.