Wireless Scheduling for Monitoring Remote Correlated Sources

Abstract

We study the design of scheduling policies to minimize monitoring error for a collection of correlated sources, where only one source can be observed at any given time. We model correlated sources as a discrete-time Wiener process, and later as a Linear Time-Invariant process, where the increments are multivariate normal random variables, with a general covariance matrix that captures the correlation structure between the sources. Under a Kalman filter-based optimal estimation framework, we show that the performance of all scheduling policies oblivious to instantaneous error can be lower and upper bounded by the weighted sum of Age of Information (AoI) across the sources for appropriately chosen weights. We use this insight to design scheduling policies that are only a constant factor away from optimality and make the rather surprising observation that AoI-based scheduling that ignores correlation is sufficient to obtain performance guarantees. We also derive scaling results that show that the optimal error scales roughly as the square of the dimensionality of the system, even in the presence of correlation. We extend these findings to processes with looser constraints. Finally, we provide simulation results to verify our claims.