The timeliness of collected information is essential for monitoring and control in data-driven intelligent infrastructures. It is typically quantified using the Age of Information (AoI) metric, which has been widely adopted to capture the freshness of information received in the form of status updates. While AoI-based metrics quantify how timely the collected information is, they largely overlook the environmental impact associated with frequent transmissions, specifically, the resulting Carbon Footprint (CF). To address this gap, we introduce a carbon-aware AoI framework. We first derive closed-form expressions for the average AoI under constrained CF budgets for the baseline $M/M/1$ and $M/M/1^*$ queuing models, assuming fixed Carbon Intensity (CI). We then extend the analysis by treating CI as a dynamic, time-varying parameter and solve the AoI minimization problem. Our results show that minimizing AoI does not inherently minimize CF, highlighting a clear trade-off between information freshness and environmental impact. CI variability further affects achievable AoI, indicating that sustainable operation requires joint optimization of CF budgets, Signal-to-noise Ratio (SNR), and transmission scheduling. This work lays the foundation for carbon-aware information freshness optimization in next-generation networks.

翻译：在数据驱动的智能基础设施中，所收集信息的时效性对于监测与控制至关重要。该特性通常通过信息年龄（Age of Information，AoI）这一度量进行量化，AoI已被广泛用于刻画以状态更新形式接收的信息的新鲜度。虽然基于AoI的度量能够量化所收集信息的及时性，但它们很大程度上忽视了频繁传输所带来的环境影响，特别是由此产生的碳足迹（Carbon Footprint，CF）。为弥补这一空白，我们提出了一个碳感知的AoI框架。我们首先在固定碳强度（Carbon Intensity，CI）的假设下，针对基准的$M/M/1$和$M/M/1^*$排队模型，推导了在受限CF预算下的平均AoI的闭式表达式。随后，我们将CI视为动态的时变参数，扩展了分析并解决了AoI最小化问题。我们的结果表明，最小化AoI并不会自然导致CF的最小化，这凸显了信息新鲜度与环境影响之间存在着明确的权衡。CI的变异性进一步影响了可实现的AoI，表明可持续运行需要对CF预算、信噪比（Signal-to-noise Ratio，SNR）以及传输调度进行联合优化。这项工作为下一代网络中碳感知的信息新鲜度优化奠定了基础。