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Age of Information Optimization and State Error Analysis for Correlated Multi-Process Multi-Sensor Systems

Egemen Erbayat, Ali Maatouk, Peng Zou, Suresh Subramaniam

TL;DR

The paper addresses timely information delivery in correlated multi-sensor, multi-process networks with a shared server. It introduces a process-centric equivalence that decomposes the system into independent two-source subsystems, derives closed-form AoI expressions for each process in an M/M/1/1 setting, and analyzes the state-estimation error via a 3D Markov model. It further proposes an optimization framework to distribute sensing probabilities across processes under sensor constraints, proving convexity in some regimes and revealing regime-switch behavior and non-convexity in others. The findings show that correlation can significantly reduce AoI and estimation error, but optimal sensing distributions can exhibit abrupt regime shifts, underscoring the need for adaptive strategies. Practically, the work informs sensor placement and sensing allocation to minimize AoI and error in correlated monitoring systems and identifies critical thresholds that trigger changes in optimal policies.

Abstract

In this paper, we examine a multi-sensor system where each sensor may monitor more than one time-varying information process and send status updates to a remote monitor over a common channel. We consider that each sensor's status update may contain information about more than one information process in the system subject to the system's constraints. To investigate the impact of this correlation on the overall system's performance, we conduct an analysis of both the average Age of Information (AoI) and source state estimation error at the monitor. Building upon this analysis, we subsequently explore the impact of the packet arrivals, correlation probabilities, and rate of processes' state change on the system's performance. Next, we consider the case where sensors have limited sensing abilities and distribute a portion of their sensing abilities across the different processes. We optimize this distribution to minimize the total AoI of the system. Interestingly, we show that monitoring multiple processes from a single source may not always be beneficial. Our results also reveal that the optimal sensing distribution for diverse arrival rates may exhibit a rapid regime switch, rather than smooth transitions, after crossing critical system values. This highlights the importance of identifying these critical thresholds to ensure effective system performance.

Age of Information Optimization and State Error Analysis for Correlated Multi-Process Multi-Sensor Systems

TL;DR

The paper addresses timely information delivery in correlated multi-sensor, multi-process networks with a shared server. It introduces a process-centric equivalence that decomposes the system into independent two-source subsystems, derives closed-form AoI expressions for each process in an M/M/1/1 setting, and analyzes the state-estimation error via a 3D Markov model. It further proposes an optimization framework to distribute sensing probabilities across processes under sensor constraints, proving convexity in some regimes and revealing regime-switch behavior and non-convexity in others. The findings show that correlation can significantly reduce AoI and estimation error, but optimal sensing distributions can exhibit abrupt regime shifts, underscoring the need for adaptive strategies. Practically, the work informs sensor placement and sensing allocation to minimize AoI and error in correlated monitoring systems and identifies critical thresholds that trigger changes in optimal policies.

Abstract

In this paper, we examine a multi-sensor system where each sensor may monitor more than one time-varying information process and send status updates to a remote monitor over a common channel. We consider that each sensor's status update may contain information about more than one information process in the system subject to the system's constraints. To investigate the impact of this correlation on the overall system's performance, we conduct an analysis of both the average Age of Information (AoI) and source state estimation error at the monitor. Building upon this analysis, we subsequently explore the impact of the packet arrivals, correlation probabilities, and rate of processes' state change on the system's performance. Next, we consider the case where sensors have limited sensing abilities and distribute a portion of their sensing abilities across the different processes. We optimize this distribution to minimize the total AoI of the system. Interestingly, we show that monitoring multiple processes from a single source may not always be beneficial. Our results also reveal that the optimal sensing distribution for diverse arrival rates may exhibit a rapid regime switch, rather than smooth transitions, after crossing critical system values. This highlights the importance of identifying these critical thresholds to ensure effective system performance.
Paper Structure (17 sections, 7 theorems, 64 equations, 9 figures, 1 table)

This paper contains 17 sections, 7 theorems, 64 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. System Simplification through Equivalence
  4. Age of Information Analysis
  5. Error Ratio Analysis
  6. Average Age Optimization
  7. Numerical Results
  8. Sensor-Process Assignment Analysis
  9. Sensing Ability-Constrained Sensor Optimization Model
  10. Conclusion
  11. Simulation Results for Impact of Buffer Length on Age of Information
  12. Proof of Lemma \ref{['Lem1']}
  13. Proof of Theorem \ref{['The1']}
  14. Proof of Lemma \ref{['Lem3']}
  15. Proof of Lemma \ref{['Lem4']}
  16. ...and 2 more sections

Key Result

Lemma 1

$\frac{}{}$ Consider a process $j$ among $M$ processes. From the monitor's perspective, the system is equivalent to Figure fig:equv_model, where there are two packet sources:

Figures (9)

  • Figure 1: Illustration of our system model.
  • Figure 2: Equivalent system model from process $j$'s perspective.
  • Figure 3: Evolution of AoI for process 1.
  • Figure 7: AoI versus $p^c_{21}$ for different $\lambda_i$ values with $\mu=4, \zeta_{1}=4,$$\zeta_{2}=4, \lambda_2 = 8$.
  • Figure 8: Error $\epsilon_1$ versus $p^c_{21}$ for different $\lambda_i$ values with $\mu=4, \lambda_2 = 8$.
  • ...and 4 more figures

Theorems & Definitions (15)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Theorem 1
  • proof
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • ...and 5 more