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 state of the source and makes a decision on whether to transmit the status updates over an unreliable channel or not. We introduce a modified randomized stationary sampling and transmission policy where the decision to perform sampling occurs probabilistically depending on the current state of the source and whether the system was in a sync state during the previous time slot or not. We then propose two new performance metrics, coined the Version Innovation Age (VIA) and the Age of Incorrect Version (AoIV) and analyze their performance under the modified randomized stationary and other state-of-the-art sampling and transmission policies. Specifically, we derive closed-form expressions for the distribution and the average of VIA, AoIV, and Age of Incorrect Information (AoII) under these policies. Furthermore, we formulate and solve three constrained optimization problems. The first optimization problem aims to minimize the average VIA subject to constraints on the time-averaged sampling cost and time-averaged reconstruction error. In the second and third problems, the objective is to minimize the average AoIV and AoII, respectively, while considering a constraint on the time-averaged sampling cost. 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.