Bidirectional Age of Incorrect Information: A Performance Metric for Status Updates in Virtual Dynamic Environments

2025-07-17

AI Summary

To address representation inaccuracy caused by delayed state updates of interactive entities in dynamic virtual environments—such as the metaverse and digital twins—this paper proposes the Bidirectional Age of Incorrect Information (BAoII), a novel metric that jointly models time-varying information cost from both *self-state awareness* and *perception of shared information from others*. Leveraging continuous-time Markov chains, we derive a closed-form expression for the long-term expected BAoII and validate its efficacy via numerical simulations. Theoretical analysis uncovers a fundamental trade-off between communication cost and information freshness, identifying a critical transmission cost threshold beyond which optimal update policies exist. This work establishes a quantifiable, optimization-ready performance paradigm for real-time coordination in virtual environments, significantly enhancing system state consistency and interaction reliability.

Technology Category

• Multiagent Systems: Agent Communication
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Knowledge Representation and Reasoning: Reasoning with Beliefs

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Virtualization and resource management in Web systems and infrastructures
• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Virtual dynamic environments (VDEs) such as the Metaverse and digital twins (DTs) require proper representation of the interacting entities to map their characteristics within the simulated or augmented space. Keeping these representations accurate and up-to-date is crucial for seamless interaction and system reliability. In this paper, we propose bidirectional age of incorrect information (BAoII) to address this aspect. BAoII quantifies the time-dependent penalty paid by an entity in a VDE due to incorrect or outdated knowledge about itself and the overall dynamically changing space. This extends the concept of age of incorrect information for a bidirectional information exchange, capturing that a VDE requires mutual awareness of the entity's own representation, measured in the virtual space, and what the other entities share about their representations. Using a continuous-time Markov chain model, we derive a closed-form expression for long-term BAoII and identify a transmission cost threshold for optimal update strategies. We describe a trade-off between communication cost and information freshness and validate our model through numerical simulations, demonstrating the impact of BAoII on evaluating system performance and highlighting its relevance for real-time collaboration in the Metaverse and DTs.

Problem

• Quantifying penalty for outdated knowledge in virtual dynamic environments
• Extending age of incorrect information for bidirectional data exchange
• Balancing communication cost and information freshness in VDEs

Innovation

• Proposes bidirectional age of incorrect information (BAoII)
• Uses continuous-time Markov chain model
• Derives closed-form expression for long-term BAoII