基于鲁棒排队方法的峰值信息年龄最坏情况近似分析

Zhongdong Liu, Yu Sang, Bin Li, Bo Ji
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引用次数: 1

摘要

一种新的时效性度量,称为信息年龄(Age-of-Information, AoI),最近吸引了许多对具有信息更新的实时应用程序的研究兴趣。它已经被广泛地研究了基于概率方法的各种排队模型,其中的分析严重依赖于特定分布的性质(例如,指数分布的无记忆性质或i.i.d.假设)。在这项工作中,我们采用了一种替代的新方法,即鲁棒排队方法,来分析峰值信息年龄(PAoI)。具体来说,我们首先使用不确定性集对随机到达和服务过程中的不确定性进行建模。这使我们能够近似非常一般的到达和服务流程的预期pai性能,包括那些表现出重尾行为或相关性的流程,在这些流程中传统的概率方法无法应用。然后,我们在单源单服务器设置中推导pai的新边界。此外,我们将我们的分析推广到具有对称到达的双源单服务器系统,这涉及到新的挑战(例如,来自两个源的更新的服务时间耦合在一个单一的不确定性集合中)。最后,通过数值实验,我们证明了我们的新边界为预期的pai提供了一个很好的近似。与文献中一些众所周知的边界(例如,基于i.i.d假设下的Kingman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都是准确的,这两种情况都是AoI性能的关键场景。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A Worst-Case Approximate Analysis of Peak Age-of-Information Via Robust Queueing Approach
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.
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