This paper considers a large-scale wireless network consisting of source-destination (SD) pairs, where the sources send time-sensitive information, termed status updates , to their corresponding destinations in a time-slotted fashion. We employ age of information (AoI) for quantifying the freshness of the status updates measured at the destination nodes under the preemptive and non-preemptive queueing disciplines with no storage facility. The non-preemptive queue drops the newly arriving updates until the update in service is successfully delivered, whereas the preemptive queue replaces the current update in service with the newly arriving update, if any. As the update delivery rate for a given link is a function of the interference field seen from the receiver, the temporal mean AoI can be treated as a random variable over space. Our goal in this paper is to characterize the spatial distribution of the mean AoI observed by the SD pairs by modeling them as a bipolar Poisson point process (PPP). Towards this objective, we first derive accurate bounds on the moments of success probability while efficiently capturing the interference-induced coupling in the activities of the SD pairs. Using this result, we then derive tight bounds on the moments as well as the spatial distribution of peak AoI (PAoI). Our numerical results verify our analytical findings and demonstrate the impact of various system design parameters on the mean PAoI.

中文翻译：

---

无线网络中信息平均峰值年龄的空间分布

本文考虑了一个由源-目的地 (SD) 对组成的大规模无线网络，其中源发送时间敏感的信息，称为 状态更新，以时隙方式更新到相应的目的地。我们使用信息年龄 (AoI) 来量化在没有存储设施的抢占式和非抢占式排队规则下在目标节点测量的状态更新的新鲜度。非抢占式队列丢弃新到达的更新，直到服务中的更新成功交付，而抢占式队列用新到达的更新（如果有）替换当前服务中的更新。由于给定链路的更新传递率是从接收器看到的干扰场的函数，因此时间平均 AoI 可以被视为空间上的随机变量。我们在本文中的目标是通过将 SD 对建模为双极泊松点过程 (PPP) 来表征 SD 对观察到的平均 AoI 的空间分布。为了这个目标，我们首先推导出成功概率时刻的准确界限，同时有效地捕获 SD 对活动中的干扰引起的耦合。使用这个结果，我们然后推导出对矩的严格界限以及峰值 AoI (PAoI) 的空间分布。我们的数值结果验证了我们的分析结果，并证明了各种系统设计参数对平均 PAoI 的影响。