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：一种名为信息龄的新时效性度量近期在涉及信息更新的实时应用中引起了广泛研究兴趣。基于概率方法，该度量已在各种排队模型中得到深入研究，但这类分析高度依赖于特定分布的性质（例如指数分布的无记忆性或独立同分布假设）。本文采用一种新兴的替代方法——鲁棒排队方法——来分析峰值信息龄。具体而言，我们首先利用不确定集合对随机到达过程和服务过程的不确定性进行建模，从而能够针对极广泛的到达和服务过程（包括呈现重尾行为或相关性的过程，而传统概率方法在此类场景中无法适用）近似其预期峰值信息龄性能。随后，我们在单源单服务器场景下推导出峰值信息龄的新上界。进一步地，我们将分析推广至具有对称到达的双源单服务器系统，该场景面临新的挑战（例如，双源更新的服务时间耦合在同一不确定集合中）。最后，通过数值实验证明，新上界能有效近似预期峰值信息龄。与文献中某些知名上界（例如基于独立同分布假设的Kingman上界在轻负载下精度不足）相比，本文提出的新近似在轻负载与高负载两种关键场景下均保持高精度，而这两种场景正是影响信息龄性能的关键工况。