Scheduling Real-Time Information-Update Flows for the Optimal Confidence in Estimation

This paper considers a wireless network where multiple flows are delivering status updates about their respective information sources. An end-user aims to make accurate real-time estimations about the status of each information source using its received packets. As the accuracy of estimation is most impacted by events in the recent past, we propose to measure the Confidence-in-Estimation by the number of timely deliveries in a window of the recent past, and say that a flow suffers from a Loss-of-Confidence (LoC) if this number is insufficient for the end user to make a reliable estimation with small confidence intervals. We then study the problem of minimizing the system-wide LoC in wireless networks where each flow has a different requirement and link quality. We show that the problem of minimizing the system-wide LoC requires the control of the temporal variance of timely deliveries for each flow. This feature makes our problem significantly different from other optimization problems that only involve the average of control variables. Surprisingly, we show that there exists a simple online scheduling algorithm that is near-optimal. Simulation results show that our proposed algorithm is significantly better than other state-of-the-art policies. The practical value of this work is further evaluated by a case study of the real-time estimation problem of linear Gaussian processes, where we show that, under the optimal estimate algorithm, our scheduling policy results in better estimate accuracy, both in terms of the average mean square error and 95-percentile of mean square error, than other policies, including one that aims to optimize Age-of-Information, another performance metric for the application of real-time estimation.