We analyze Age of Information (AoI) in wireless networks where nodes use a spatially adaptive random access scheme to send status updates to a central base station. We show that the set of achievable AoI in this setting is convex, and design policies to minimize weighted sum, min-max, and proportionally fair AoI by setting transmission probabilities as a function of node locations. We show that under the capture model, when the spatial topology of the network is considered, AoI can be significantly improved, and we obtain tight performance bounds on weighted sum and min-max AoI. Finally, we design a policy where each node sets its transmission probability based only on its own distance from the base station, when it does not know the positions of other nodes, and show that it converges to the optimal proportionally fair policy as the size of the network goes to infinity.

翻译：我们分析无线网络的信息年龄(AoI),在无线网络中,节点使用空间适应性随机访问计划向中央基地站发送状态更新。我们显示,在这个环境中,一套可实现的AoI是二次曲线,设计政策,通过将传输概率设定为节点的函数来尽量减少加权和最小最大和比例公平的AoI。我们显示,在捕捉模式下,当考虑网络的空间表层学时,AoI可以大大改进,我们获得加权和最小最大AoI的严格性能约束。最后,我们设计了一种政策,即当每个节点不知道其他节点的位置时,每个节点只能根据它自己距离基地站的距离设定其传输概率,并显示它会随着网络规模的无限化而与最佳比例公平政策趋同。