A new timeliness metric, called Age-of-Information (AoI), has recently attracted a lot of research interests for real-time applications with information updates. It has been extensively studied for various queueing models based on the probabilistic approaches, where the analyses heavily depend on the properties of specific distributions (e.g., the memoryless property of the exponential distribution or the i.i.d. assumption). In this work, we take an alternative new approach, the robust queueing approach, to analyze the Peak Age-of-Information (PAoI). Specifically, we first model the uncertainty in the stochastic arrival and service processes using uncertainty sets. This enables us to approximate the expected PAoI performance for very general arrival and service processes, including those exhibiting heavy-tailed behaviors or correlations, where traditional probabilistic approaches cannot be applied. We then derive a new bound on the PAoI in the single-source single-server setting. Furthermore, we generalize our analysis to two-source single-server systems with symmetric arrivals, which involves new challenges (e.g., the service times of the updates from two sources are coupled in one single uncertainty set). Finally, through numerical experiments, we show that our new bounds provide a good approximation for the expected PAoI. Compared to some well-known bounds in the literature (e.g., one based on Kingman's bound under the i.i.d. assumption) that tends to be inaccurate under light load, our new approximation is accurate under both light and high loads, both of which are critical scenarios for the AoI performance.

翻译：一种名为信息年龄（Age-of-Information，AoI）的新型时效性度量方法，近年来在具有信息更新的实时应用领域引起了广泛研究兴趣。基于概率方法，已有大量研究针对各种排队模型展开分析，但这些分析高度依赖于特定分布的属性（例如指数分布的无记忆性或独立同分布假设）。本文采用一种替代性的新方法——鲁棒排队方法——来分析峰值信息年龄（Peak Age-of-Information，PAoI）。具体而言，我们首先利用不确定集合对随机到达和服务过程中的不确定性进行建模。这使得我们能够针对非常一般的到达和服务过程（包括具有重尾行为或相关性的过程）近似期望PAoI性能，而传统概率方法无法应用于此类场景。随后，我们在单源单服务器场景中推导了PAoI的一个新边界。此外，我们将分析推广至具有对称到达的双源单服务器系统，这带来了新的挑战（例如两个源更新服务的服务时间耦合于单一不确定集合中）。最后，通过数值实验，我们证明新边界可对期望PAoI提供良好近似。与文献中一些已知边界（例如基于独立同分布假设下Kingman界的边界）在轻负载下往往不准确相比，我们的新近似在轻负载和高负载下均保持精确，而这两种负载场景对AoI性能均至关重要。