How Far Back in Time a Digital Twin Reflects the State of the Physical Object: Age of Staleness

2026-05-15

AI Summary

This work addresses the limitations of existing information freshness metrics, such as Age of Information (AoI), which neglect physical dynamics and semantic accuracy, thereby inadequately capturing the timeliness of digital twin states. To overcome this, the paper introduces a novel metric termed Age of Staleness (AoS), which jointly incorporates semantic accuracy and temporal freshness to quantify how recently a digital twin last accurately reflected its physical counterpart. Leveraging a Markovian source model, the authors derive a closed-form expression for AoS in the single-source case and prove its monotonic decrease with increasing sampling rate. For multi-source scenarios under a total sampling-rate constraint, they formulate a multivariate non-convex optimization problem and employ monotonicity-based algorithms—such as the polyblock method—to achieve near-optimal sampling allocation. This approach substantially enhances both timeliness and fidelity in digital twin monitoring, effectively overcoming the semantic blindness inherent in conventional AoI-based frameworks.

Abstract

The groundbreaking metric age of information (AoI) has been introduced to measure information freshness in communication networks. As transformational as it is, AoI metric falls short in some applications, such as remote monitoring, since it is a semantic-agnostic metric which does not consider the dynamics of the random process. There is a need to quantify the performance of a remote estimator via a metric that combines freshness and semantic aspects. To this end, in this paper, we introduce a novel metric coined age of staleness (AoS) that measures when the last time that the current estimation was correct. First, we analyze a simple scenario where an $n$-ary symmetric Markov source is observed by a monitor via a constant sampling rate, obtain a closed-form expression for the AoS, and show that it is a monotonically decreasing function of the sampling rate. Next, we consider multiple distinct Markov sources, and formulate an optimization problem, where the remote monitor allocates the total sampling rate to tracking the sources. Although the optimization problem is non-convex, its structure is suitable for obtaining a near-optimal solution using the polyblock algorithm, which leverages the monotonicity of the objective function. While the new AoS metric could be applicable in many scenarios, we believe it is particularly well-suited for a digital twin network (DTN) where multiple physical objects (POs) are monitored with a total sampling rate constraint to maintain a digital representation of them, namely, their digital twin (DT).

Problem

• age of staleness
• digital twin
• remote monitoring
• information freshness
• Markov sources

Innovation

• Age of Staleness
• Digital Twin Network
• Remote Estimation
• Sampling Rate Allocation
• Markov Source