Age of Information Analysis for Dynamic Spectrum Sharing Timely information updates are critical to timesensitive applications in networked monitoring and control systems. In this paper, the problem of realtime status update is considered for a cognitive radio network (CRN), in which the secondary user (SU) can relay the status packets from the primary user (PU) to the destination. In the considered CRN, the SU has opportunities to access the spectrum owned by the PU to send its own status packets to the destination. The freshness of information is measured by the age of information (AoI) metric. The problem of minimizing the average AoI and energy consumption by developing new optimal status update and packet relaying schemes for the SU is addressed under an average AoI constraint for the PU. This problem is formulated as a constrained Markov decision process (CMDP). The monotonic and decomposable properties of the value function are characterized and then used to show that the optimal update and relaying policy is thresholdbased with respect to the AoI of the SU. These structures reveal a tradeoff between the AoI of the SU and the energy consumption as well as between the AoI of the SU and the AoI of the PU. An asymptotically optimal algorithm is proposed. Numerical results are then used to show the effectiveness of the proposed policy.

Minimizing Age of Information for RealTime Monitoring in ResourceConstrained Industrial IoT Networks This paper considers an Industrial Internet of Thing (IIoT) system with a source monitoring a dynamic process with randomly generated status updates. The status updates are sent to an designated destination in a realtime manner over an unreliable link. The source is subject to a practical constraint of limited average transmission power. Thus, the system should carefully schedule when to transmit a fresh status update or retransmit the stale one. To characterize the performance of timely status update, we adopt a recent concept, Age of Information (AoI), as the performance metric. We aim to minimize the longterm average AoI under the limited average transmission power at the source, by formulating a constrained Markov Decision Process (CMDP) problem. To address the formulated CMDP, we recast it into an unconstrained Markov Decision Process (MDP) through Lagrangian relaxation. We prove the existence of optimal stationary policy of the original CMDP, which is a randomized mixture of two deterministic stationary policies of the unconstrained MDP. We also explore the characteristics of the problem to reduce the action space of each state to significantly reduce the computation complexity. We further prove the threshold structure of the optimal deterministic policy for the unconstrained MDP. Simulation results show the proposed optimal policy achieves lower average AoI compared with random policy, especially when the system suffers from stricter resource constraint. Besides, the influence of status generation probability and transmission failure rate on optimal policy and the resultant average AoI as well as the impact of average transmission power on the minimal average AoI are unveiled.