  In this paper, we investigate a model relevant to semantics-aware
goal-oriented communications, and we propose a new metric that incorporates the
utilization of information in addition to its timelines. Specifically, we
consider the transmission of observations from an external process to a
battery-powered receiver through status updates. These updates inform the
receiver about the process status and enable actuation if sufficient energy is
available to achieve a goal. We focus on a wireless power transfer (WPT) model,
where the receiver receives energy from a dedicated power transmitter and
occasionally from the data transmitter when they share a common channel. We
analyze the Age of Information (AoI) and propose a new metric, the \textit{Age
of Actuation (AoA), which is relevant when the receiver utilizes the status
updates to perform actions in a timely manner}. We provide analytical
characterizations of the average AoA and the violation probability of the AoA,
demonstrating that AoA generalizes AoI. Moreover, we introduce and analytically
characterize the \textit{Probability of Missing Actuation (PoMA)}; this metric
becomes relevant also \textit{to quantify the incurred cost of a missed
action}. We formulate unconstrained and constrained optimization problems for
all the metrics and present numerical evaluations of our analytical results.
This proposed set of metrics goes beyond the traditional timeliness metrics
since the synergy of different flows is now considered.
