Minimum Age of Information in the Internet of Things with Non-uniform Status Packet Sizes

In this paper, a real-time Internet of Things (IoT) monitoring system is considered in which the IoT devices are scheduled to sample underlying physical processes and send the status updates to a common destination. In a real-world IoT, due to the possibly different dynamics of each physical process, the sizes of the status updates for different devices are often different and each status update typically requires multiple transmission slots. By taking into account such multi-time slot transmissions with non-uniform sizes of the status updates under noisy channels, the problem of joint device scheduling and status sampling is studied in order to minimize the average age of information (AoI) at the destination. This stochastic problem is formulated as an infinite horizon average cost Markov decision process (MDP). The monotonicity of the value function of the MDP is characterized and then used to show that the optimal scheduling and sampling policy is threshold-based with respect to the AoI at each device. To overcome the curse of dimensionality, a low-complexity suboptimal policy is proposed through a semi-randomized base policy and linear approximated value functions. The proposed suboptimal policy is shown to exhibit a similar structure to the optimal policy, which provides a structural base for its effective performance. A structure-aware algorithm is then developed to obtain the suboptimal policy. The analytical results are further extended to the IoT monitoring system with random status update arrivals, for which, the optimal scheduling and sampling policy is also shown to be threshold-based with the AoI at each device. Simulation results illustrate the structures of the optimal policy and show a near-optimal AoI performance resulting from the proposed suboptimal solution approach.