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.

翻译：本文研究了一种与语义感知目标导向通信相关的模型，并提出了一种新指标，该指标在考虑信息及时性的同时融入了信息的利用。具体而言，我们考虑了通过状态更新将外部过程的观测结果传输至电池供电的接收器。这些更新告知接收器过程状态，并在有足够能量实现目标时支持执行操作。我们聚焦于无线能量传输（WPT）模型，其中接收器从专用能量发射器接收能量，偶尔在共享信道时从数据发射器获取能量。我们分析了信息年龄（AoI），并提出了新指标——执行年龄（AoA），该指标与接收器利用状态更新及时执行动作的场景相关。我们给出了平均AoA及其违反概率的解析表征，证明AoA是AoI的泛化形式。此外，我们引入并解析表征了缺失执行概率（PoMA）；该指标同样用于量化缺失动作产生的代价。针对所有指标，我们构建了无约束与有约束优化问题，并对解析结果进行了数值评估。所提出的指标集超越了传统及时性指标，因为现在考虑了不同信息流的协同效应。