AoI-based Optimal Transmission Scheduling for Multi-process Remote Estimation

We investigate multi-process remote estimation systems where sensors transmit sampling data of the physical processes to a remote estimator through a shared communication channel subject to the uncertain transmission time. Due to channel resource constraint, at most one sensor can transmit at a time. Therefore, for the sake of optimal estimation performance, it is required to address, for each sensor, when to perform sampling and when to transmit data. In this paper, leveraging the recently emerged notion of age of information (AoI), we show that such a problem of joint sampling and transmission scheduling degenerates into an optimal waiting time problem by rigorously proving that greedily selecting the sensor to transmit data is optimal and independent of the waiting time decision. We further derive an explicit expression of the optimal waiting time policy when the processes and sensors are homogeneous, and show that the optimal policy reduces to the intuitively-optimal zero-wait policy only in some special cases. Upon extending our analysis to heterogeneous contexts, we articulate a structured qualitative outline of the optimal transmission scheduling policy and corroborate its empirical compatibility with the zero-wait principle. Simulation results validate the optimality of the proposed policy.