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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 multiconnectivity 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.
Cao et al. (Wed,) studied this question.