Monitoring Correlated Sources: AoI-based Scheduling is Nearly Optimal

TL;DR

This work analyzes scheduling for monitoring M correlated Gaussian sources over a capacity-constrained link, where a single sensor can transmit per slot. By exploiting a Kalman-filter estimator under oblivious scheduling, it establishes upper and lower bounds on monitoring error in terms of a weighted AoI across sources, even in the presence of correlation. It then designs Max-Weight style policies (Maximum Expected Error and Maximum Weighted Age) that achieve constant-factor optimality with respect to the optimal oblivious scheduler, showing AoI-based scheduling suffices despite correlations. The paper further extends results to diagonal and general A matrices, derives scaling laws indicating near-quadratic growth in error with system dimensionality, and verifies claims through extensive simulations across Wiener-process and diagonal-A scenarios. Overall, AoI remains a robust, low-complexity criterion for near-optimal monitoring of correlated dynamic sources in networked systems.

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, 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. Finally, we provide simulation results to verify our claims.

Figures (6)

• Figure 1: $M$ sensors tracking $M$ processes which are correlated. The central monitor can communicate with sensors one at a time, due to interference constraints.
• Figure 2: Upper and lower bounds demonstrated for $M = 20$ sensors. The scheduling process is the optimal stationary randomized schedulekadota_scheduling_2018. The $Q$ matrix represents a highly correlated setting, where the diagonal elements are $q_{ii} = 1$, and the non-diagonal elements are $q_{ij} = 0.8$.
• Figure 3: Comparison of long-term average expected error of scheduling policies for the correlation structure defined in section \ref{['subsection:symm_cov_matrices']} with $\rho = 0.8$
• Figure 4: Comparison of long term average expected error of scheduling policies for the correlation structure defined in section \ref{['subsection:asymm_cov_matrices']} with $\rho = 0.8$
• Figure 5: Comparison of long term average expected error of scheduling policies for the correlation structure defined in subsection \ref{['subsection:row_changing']}.

Theorems & Definitions (42)

• Lemma 1
• proof
• Theorem 1
• proof
• Theorem 2
• proof
• Theorem 3
• proof : Proof of Theorem \ref{['thm:order_of_mag_full']}
• Theorem 4
• proof