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This paper considers an Industrial Internet of Thing (IIoT) system with asource monitoring a dynamic process with randomly generated status updates. Thestatus updates are sent to an designated destination in a real-time manner overan unreliable link. The source is subject to a practical constraint of limitedaverage transmission power. Thus, the system should carefully schedule when totransmit a fresh status update or retransmit the stale one. To characterize theperformance of timely status update, we adopt a recent concept, Age ofInformation (AoI), as the performance metric. We aim to minimize the long-termaverage AoI under the limited average transmission power at the source, byformulating a constrained Markov Decision Process (CMDP) problem. To addressthe formulated CMDP, we recast it into an unconstrained Markov Decision Process(MDP) through Lagrangian relaxation. We prove the existence of optimalstationary policy of the original CMDP, which is a randomized mixture of twodeterministic stationary policies of the unconstrained MDP. We also explore thecharacteristics of the problem to reduce the action space of each state tosignificantly reduce the computation complexity. We further prove the thresholdstructure of the optimal deterministic policy for the unconstrained MDP.Simulation results show the proposed optimal policy achieves lower average AoIcompared with random policy, especially when the system suffers from stricterresource constraint. Besides, the influence of status generation probabilityand transmission failure rate on optimal policy and the resultant average AoIas well as the impact of average transmission power on the minimal average AoIare unveiled.

Minimizing Age of Information for Real-Time Monitoring in Resource-Constrained Industrial IoT Networks