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

TL;DR

This paper introduces the Age of Actuated Information (AoAI), a new metric for measuring the timeliness of actions in control systems, and analyzes its behavior alongside the existing AoA metric under various buffering and actuation scenarios.

Contribution

The paper proposes AoAI as a novel metric, derives closed-form expressions for AoA and AoAI in discrete-time systems, and characterizes the steady-state distribution of a Geo/Geo/1 queue, revealing insights into actuation timeliness.

Findings

AoAI differs from AoA in buffered systems.

Increasing update or actuation rates can degrade timeliness.

Closed-form steady-state distribution of Geo/Geo/1 queue obtained.

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.