Semantics in Actuation Systems: From Age of Actuation to Age of Actuated Information

TL;DR

This work addresses end-to-end action timeliness in actuation systems where data reception, actuation permissions, and energy availability jointly govern when actions occur. It extends the Age of Information framework by introducing the Age of Actuated Information (AoAI) alongside an upgraded Age of Actuation (AoA), and derives closed-form expressions for AoI, AoA, and AoAI across four discrete-time queueing scenarios, including buffering and energy harvesting. The results reveal that AoAI generally dominates AoI and AoA in buffered systems, while AoA and AoI coincide under instantaneous actuation; buffering can induce counterintuitive regimes where higher update or actuation rates degrade timeliness. Additionally, the paper provides a novel closed-form characterization of the steady-state distribution of a Geo/Geo/1 FCFS queue in terms of queue length and head-of-line age, offering new analytical tools for semantic, goal-oriented networks and guidance for system design under energy and permission constraints.

Abstract

In this paper, we study the timeliness of actions in communication systems where actuation is constrained by control permissions or energy availability. Building on the Age of Actuation (AoA) metric, which quantifies the timeliness of actions independently of data freshness, we introduce a new metric, the \emph{Age of Actuated Information (AoAI)}. AoAI captures the end-to-end timeliness of actions by explicitly accounting for the age of the data packet at the moment it is actuated. We analyze and characterize both AoA and AoAI in discrete-time systems with data storage capabilities under multiple actuation scenarios. The actuator requires both a data packet and an actuation opportunity, which may be provided by a controller or enabled by harvested energy. Data packets may be stored either in a single-packet buffer or an infinite-capacity queue for future actuation. For these settings, we derive closed-form expressions for the average AoA and AoAI and investigate their structural differences. While AoA and AoAI coincide in instantaneous actuation systems, they differentiate when data buffering is present. Our results reveal counterintuitive regimes in which increasing update or actuation rates degrade action timeliness for both AoA and AoAI. Moreover, as part of the analysis, we obtain a novel closed-form characterization of the steady-state distribution of a Geo/Geo/1 queue operating under the FCFS discipline, expressed solely in terms of the queue length and the age of the head-of-line packet. The proposed metrics and analytical results provide new insights into the semantics of timeliness in systems where information ultimately serves the purpose of actuation.

Figures (6)

• Figure 1: The considered system model in three cases that capture different aspects.
• Figure 2: Sample paths and their corresponding events and processes for the concurrent evolution of the AoI, AoA, and AoAI, for the three scenarios mentioned on each figure.
• Figure 3: A sample path and its corresponding events and processes for the concurrent evolution of the AoI, AoA, and AoAI for the Geo/Geo/1/1 with a battery.
• Figure 4: The average AoAI, for the Geo/Geo/1 under FCFS policy with a controller.
• Figure 5: The average AoA, for the Geo/Geo/1/1 with a battery, for different values of $\lambda_2$ against $\lambda_1$ and the optimum values of $\lambda_1$.

Theorems & Definitions (14)

• Theorem 1
• proof
• Remark 1
• Remark 2
• Theorem 2
• proof
• Remark 3
• Remark 4
• Definition 1: Queue Markov Process and Queue State
• Theorem 3