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Age of Actuated Information and Age of Actuation in a Data-Caching Energy Harvesting Actuator

Ali Nikkhah, Anthony Ephremides, Nikolaos Pappas

TL;DR

This paper defines two timeliness metrics, AoA and AoAI, to quantify action timeliness and data-freshness for actuations in a data-caching energy-harvesting system. It develops a discrete-time, cache- and battery-constrained model and analyzes AoI, AoA, and AoAI using Markov chains, including a three-dimensional framework to obtain stationary distributions and closed-form averages. The key findings show that AoAI decreases with data and energy arrival rates, while AoA can exhibit non-monotonic behavior under scarce resources, underscoring a fundamental distinction between action timeliness and data freshness. These results, supported by simulations, provide design insights for semantics-aware, resource-constrained actuation in IoT and autonomous systems.

Abstract

In this paper, we introduce two metrics, namely, age of actuation (AoA) and age of actuated information (AoAI), within a discrete-time system model that integrates data caching and energy harvesting (EH). AoA evaluates the timeliness of actions irrespective of the age of the information, while AoAI considers the freshness of the utilized data packet. We use Markov Chain analysis to model the system's evolution. Furthermore, we employ three-dimensional Markov Chain analysis to characterize the stationary distributions for AoA and AoAI and calculate their average values. Our findings from the analysis, validated by simulations, show that while AoAI consistently decreases with increased data and energy packet arrival rates, AoA presents a more complex behavior, with potential increases under conditions of limited data or energy resources. These metrics go towards the semantics of information and goal-oriented communications since they consider the timeliness of utilizing the information to perform an action.

Age of Actuated Information and Age of Actuation in a Data-Caching Energy Harvesting Actuator

TL;DR

This paper defines two timeliness metrics, AoA and AoAI, to quantify action timeliness and data-freshness for actuations in a data-caching energy-harvesting system. It develops a discrete-time, cache- and battery-constrained model and analyzes AoI, AoA, and AoAI using Markov chains, including a three-dimensional framework to obtain stationary distributions and closed-form averages. The key findings show that AoAI decreases with data and energy arrival rates, while AoA can exhibit non-monotonic behavior under scarce resources, underscoring a fundamental distinction between action timeliness and data freshness. These results, supported by simulations, provide design insights for semantics-aware, resource-constrained actuation in IoT and autonomous systems.

Abstract

In this paper, we introduce two metrics, namely, age of actuation (AoA) and age of actuated information (AoAI), within a discrete-time system model that integrates data caching and energy harvesting (EH). AoA evaluates the timeliness of actions irrespective of the age of the information, while AoAI considers the freshness of the utilized data packet. We use Markov Chain analysis to model the system's evolution. Furthermore, we employ three-dimensional Markov Chain analysis to characterize the stationary distributions for AoA and AoAI and calculate their average values. Our findings from the analysis, validated by simulations, show that while AoAI consistently decreases with increased data and energy packet arrival rates, AoA presents a more complex behavior, with potential increases under conditions of limited data or energy resources. These metrics go towards the semantics of information and goal-oriented communications since they consider the timeliness of utilizing the information to perform an action.
Paper Structure (11 sections, 2 theorems, 28 equations, 7 figures, 1 table)

This paper contains 11 sections, 2 theorems, 28 equations, 7 figures, 1 table.

Table of Contents

  1. Introduction
  2. System Model
  3. Analytical Results
  4. Age of Information (AoI)
  5. Age of Actuation (AoA)
  6. Age of Actuated Information (AoAI)
  7. The relations between the AoI, AoA, and AoAI
  8. Numerical and Simulation Results
  9. Conclusion
  10. Proof of the Theorem 1: The Average AoA
  11. Proof of the Theorem 2: The Average AoAI

Key Result

Theorem 1

The average AoA is given by (Average_AoA) at the top of this page.

Figures (7)

  • Figure 1: The considered system model.
  • Figure 2: A sample path of the evolution of AoAI, AoA, and AoI.
  • Figure 3: The average AoA versus $\lambda_1$ and $\lambda_2$.
  • Figure 4: The average AoA for the different values of $\lambda_2$ versus $\lambda_1$.
  • Figure 5: The average AoA for $\lambda_2=0.1$ versus $\lambda_1$.
  • ...and 2 more figures

Theorems & Definitions (5)

  • Theorem 1
  • proof
  • Theorem 2
  • proof
  • Remark 1