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 the IoT devices sample a physical process with a sampling cost and send the status packet to a given destination with an updating cost. This joint status sampling and updating process is designed to minimize the average age of information (AoI) at the destination node under an average energy cost constraint at each device. This stochastic problem is formulated as an infinite horizon average cost constrained Markov decision process (CMDP) and transformed into an unconstrained Markov decision process (MDP) using a Lagrangian method. For the single IoT device case, the optimal policy for the CMDP is shown to be a randomized mixture of two deterministic policies for the unconstrained MDP, which is of threshold type. This reveals a fundamental tradeoff between the average AoI at the destination and the sampling and updating costs. Then, a structure-aware optimal algorithm to obtain the optimal policy of the CMDP is proposed and the impact of the wireless channel dynamics is studied while demonstrating that channels having a larger mean channel gain and less scattering can achieve better AoI performance. For the case of multiple IoT devices, a low-complexity semi-distributed suboptimal policy is proposed with the updating control at the destination and the sampling control at each IoT device. Then, an online learning algorithm is developed to obtain this policy, which can be implemented at each IoT device and requires only the local knowledge and small signaling from the destination. The proposed learning algorithm is shown to converge almost surely to the suboptimal policy. Simulation results show the structural properties of the optimal policy for the single IoT device case; and show that the proposed policy for multiple IoT devices outperforms a zero-wait baseline policy, with average AoI reductions reaching up to 33%. Index Terms-Internet of things, status update, age of information, Markov decision processes, structural analysis, distributed stochastic learning.
In REF , both single source system and multiple source system were considered and the sampling and updating to minimize the average AoI for systems was jointly designed under an energy constraint by resorting to the MDP tool.
Joint Status Sampling and Updating for Minimizing Age of Information in the Internet of Things
IEEE Transactions on Communications
IEEE Transactions on Communications
Mathematics Computer Science