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:一个新的及时性指标(AoI)最近吸引了许多研究兴趣来实时应用信息更新的实时应用程序(AoI),根据概率方法对各种排队模式进行了广泛研究,分析在很大程度上取决于特定分布的特性(例如指数分布或i.i.d.假设的无记忆属性)。在这项工作中,我们采取了另一种新办法,即强有力的排队方法,以分析峰值信息时代(PaoI) 。具体地说,我们首先用不确定性组来模拟随机到货和服务流程的不确定性。这使我们能够在非常普遍的到货和服务流程中,包括显示重到货行为或相关性(例如指数分布或i.d.假设的无记忆性能)。在单一源单一服务器的设置中,我们对PaoI有新的约束性。我们把我们的分析概括为两个源的单服务器系统,有对齐的到货的到货和服务的到货过程,其中都包含新的挑战(例如,在国王到货的预测性能中,我们从预估量的两处,我们从预估测的到一个数值的两处,我们之间的服务源的到一个新的到一个直估值。最后的到一个根据IM的到一个基的到一个基的到一个基的到预的到一个基数的到一个的到一个的到比值。