Age of information (AoI) has been widely accepted as a measure quantifying freshness of status information in real-time status update systems. In many of such systems, multiple sources share a limited network resource and therefore the AoIs defined for the individual sources should be correlated with each other. However, there are not found any results studying the correlation of two or more AoIs in a status update system with multiple sources. In this work, we consider a multi-source system sharing a common service facility and provide a framework to investigate joint performance of the multiple AoIs. We then apply our framework to a simple pushout server with multiple sources and derive a closed-form formula of the joint Laplace transform of the AoIs in the case with independent M/G inputs. We further show some properties of the correlation coefficient of AoIs in the two-source system.

中文翻译：

---

多源推送服务器信息年龄联合性能分析

信息时代 (AoI) 已被广泛接受作为量化实时状态更新系统中状态信息新鲜度的度量。在许多这样的系统中，多个源共享有限的网络资源，因此为各个源定义的 AoI 应该相互关联。然而，在具有多个来源的状态更新系统中，没有发现任何研究两个或多个 AoI 相关性的结果。在这项工作中，我们考虑了一个共享公共服务设施的多源系统，并提供了一个框架来研究多个 AoI 的联合性能。然后，我们将我们的框架应用于具有多个源的简单推送服务器，并在具有独立 M/G 输入的情况下推导出 AoI 的联合拉普拉斯变换的封闭形式公式。