  In this work, we study the problem of real-time tracking and reconstruction
of an information source with the purpose of actuation. A device monitors an
$N$-state Markov process and transmits status updates to a receiver over a
wireless erasure channel. We consider a set of joint sampling and transmission
policies, including a semantics-aware one, and we study their performance with
respect to relevant metrics. Specifically, we investigate the real-time
reconstruction error and its variance, the consecutive error, the cost of
memory error, and the cost of actuation error. Furthermore, we propose a
randomized stationary sampling and transmission policy and derive closed-form
expressions for all aforementioned metrics. We then formulate an optimization
problem for minimizing the real-time reconstruction error subject to a sampling
cost constraint. Our results show that in the scenario of constrained sampling
generation, the optimal randomized stationary policy outperforms all other
sampling policies when the source is rapidly evolving. Otherwise, the
semantics-aware policy performs the best.
