While information delivery in industrial Internet of things demands reliability and latency guarantees, the freshness of the controllers available information, measured by the age of information (AoI), is paramount for high-performing industrial automation. The problem in this work is cast as a sensors transmit power minimization subject to the peak-AoI requirement and a probabilistic constraint on queuing latency. We further characterize the tail behavior of the latency by a generalized Pareto distribution (GPD) for solving the power allocation problem through Lyapunov optimization. As each sensor utilizes its own data to locally train the GPD model, we incorporate federated learning and propose a local-model selection approach which accounts for correlation among the sensors training data. Numerical results show the tradeoff between the transmit power, peak AoI, and delays tail distribution. Furthermore, we verify the superiority of the proposed correlation-aware approach for selecting the local models in federated learning over an existing baseline.
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