Age of Information (AoI) has been proposed to quantify the freshness of information for emerging real-time applications such as remote monitoring and control in wireless networked control systems (WNCSs). Minimization of the average AoI and its outage probability can ensure timely and stable transmission. Energy efficiency (EE) also plays an important role in WNCSs, as many devices are featured by low cost and limited battery. Multi-connectivity over multiple links enables a decrease in AoI, at the cost of energy. We tackle the unresolved problem of selecting the optimal number of connections that is both AoI-optimal and energy-efficient, while avoiding risky states. To address this issue, the average AoI and peak AoI (PAoI), as well as PAoI violation probability are formulated as functions of the number of connections. Then the EE-PAoI ratio is introduced to allow a tradeoff between AoI and energy, which is maximized by the proposed risk-aware, AoI-optimal and energy-efficient connectivity scheme. To obtain this, we analyze the property of the formulated EE-PAoI ratio and prove the monotonicity of PAoI violation probability. Interestingly, we reveal that the multi-connectivity scheme is not always preferable, and the signal-to-noise ratio (SNR) threshold that determines the selection of the multi-connectivity scheme is derived as a function of the coding rate. Also, the optimal number of connections is obtained and shown to be a decreasing function of the transmit power. Simulation results demonstrate that the proposed scheme enables more than 15 folds of EE-PAoI gain at the low SNR than the single-connectivity scheme.

翻译：信息年龄（AoI）被提出用于量化新兴实时应用（如无线网络控制系统（WNCS）中的远程监控与控制）的信息新鲜度。最小化平均AoI及其中断概率可确保传输的及时性与稳定性。能效（EE）在WNCS中也具有重要意义，因为许多设备具有低成本、电池容量有限的特点。多链路的多连接能够降低AoI，但代价是能耗增加。我们解决了在避免高风险状态的同时，选择既满足AoI最优又节能的最佳连接数这一未解问题。为此，将平均AoI、峰值AoI（PAoI）及PAoI违规概率建模为连接数的函数，进而引入EE-PAoI比率以权衡AoI与能耗，并通过所提出的风险感知、AoI最优且节能的连接方案实现该比率的最大化。为达成此目标，我们分析了所建EE-PAoI比率的性质，并证明了PAoI违规概率的单调性。有趣的是，我们揭示了多连接方案并非始终最优，并推导出决定多连接方案选择的信噪比（SNR）阈值作为编码率的函数。同时，得到了最佳连接数，并证明其随发射功率增加而递减。仿真结果表明，在低信噪比下，所提方案相比单连接方案实现了超过15倍的EE-PAoI增益。