Optimal Sampling and Updating for Minimizing Age of Information in the Internet of Things

The effective operation of time-critical Internet of things (IoT) applications requires real-time reporting of fresh status information of underlying physical processes. In this paper, a real-time IoT monitoring system is considered, in which an IoT device samples a physical process with a sampling cost and sends the status packet to a given destination with an updating cost. The optimal status sampling and updating process is designed to minimize the average age of information (AoI) at the destination under an average energy cost constraint at the device. This stochastic optimization problem is formulated as an infinite horizon average cost constrained Markov decision process (CMDP). Using a Lagrangian method, the CMDP is transformed into an unconstrained Markov decision process (MDP), where the optimal policy for the CMDP is a randomized mixture of two deterministic policies for the unconstrained MDP. It is shown that the optimal policy for the unconstrained MDP is of threshold type with respect to the AoI state of the device and the AoI state of the destination. This reveals a fundamental tradeoff between the average AoI of the destination and the sampling and updating costs. Then, a structure-aware algorithm is proposed to obtain the optimal policy for the CMDP. Finally, the impact of the wireless channel dynamics on the system performance is studied while demonstrating that channels having a large mean channel gain and less scattering can achieve better AoI performance.