Unifying AoI Minimization and Remote Estimation - Optimal Sensor/Controller Coordination with Random Two-way Delay

The ubiquitous usage of communication networks in modern sensing and control applications has kindled new interests on the timing-based coordination between sensors and controllers, i.e., how to use the "waiting time" to improve the system performance. Contrary to the common belief that a zero-wait policy is always optimal, Sun et al. showed that a controller can strictly improve the data freshness, the so-called Age-of-Information (AoI), by postponing transmission in order to lengthen the duration of staying in a good state. The optimal waiting policy for the sensor side was later characterized in the context of remote estimation. Instead of focusing on the sensor and controller sides separately, this work develops the optimal joint sensor/controller waiting policy in a Wiener-process system. The results can be viewed as strict generalization of the above two important results in the sense that not only do we consider joint sensor/controller designs (as opposed to sensor-only or controller-only schemes), but we also assume random delay in both the forward and feedback directions (as opposed to random delay in only one direction). In addition to provable optimality, extensive simulation is used to verify the performance of the proposed scheme in various settings.