We consider a fully-connected wireless gossip network which consists of a source and $n$ receiver nodes. The source updates itself with a Poisson process and also sends updates to the nodes as Poisson arrivals. Upon receiving the updates, the nodes update their knowledge about the source. The nodes gossip the data among themselves in the form of Poisson arrivals to disperse their knowledge about the source. The total gossiping rate is bounded by a constraint. The goal of the network is to be as timely as possible with the source. We propose a scheme which we coin \emph{age sense updating multiple access in networks (ASUMAN)}, which is a distributed opportunistic gossiping scheme, where after each time the source updates itself, each node waits for a time proportional to its current age and broadcasts a signal to the other nodes of the network. This allows the nodes in the network which have higher age to remain silent and only the low-age nodes to gossip, thus utilizing a significant portion of the constrained total gossip rate. We calculate the average age for a typical node in such a network with symmetric settings, and show that the theoretical upper bound on the age scales as $O(1)$. ASUMAN, with an average age of $O(1)$, offers significant gains compared to a system where the nodes just gossip blindly with a fixed update rate, in which case the age scales as $O(\log n)$. Further, we analyzed the performance of ASUMAN for fractional, finitely connected, sublinear and hierarchical cluster networks. Finally, we show that the $O(1)$ age scaling can be extended to asymmetric settings as well. We give an example of power law arrivals, where nodes' ages scale differently but follow the $O(1)$ bound.

翻译：我们考虑一个由源节点和$n$个接收节点组成的全连接无线闲谈网络。源节点通过泊松过程自我更新，并以泊松到达方式向节点发送更新。节点接收更新后更新其对源节点的认知。节点间以泊松到达方式相互闲谈，以传播其对源节点的认知。闲谈总速率受限于一个约束条件。网络的目标是尽可能与源节点保持时效同步。我们提出一种名为"网络中的年龄感知更新多址接入（ASUMAN）"的方案，这是一种分布式机会式闲谈方案：每次源节点更新自身状态后，每个节点会等待与其当前年龄成正比的时间，随后向网络中其他节点广播信号。这种机制使网络中年龄较大的节点保持沉默，仅允许低年龄节点进行闲谈，从而有效利用受约束的总闲谈速率的大部分带宽。我们计算了对称设置下典型节点的平均年龄，并证明年龄的理论上界标度为$O(1)$。平均年龄为$O(1)$的ASUMAN方案相比节点以固定更新速率盲目闲谈的系统（后者年龄标度为$O(\log n)$）实现了显著增益。此外，我们分析了ASUMAN在分式连接、有限连接、次线性连接及分层集群网络中的性能。最后，我们证明$O(1)$的年龄标度可扩展至非对称设置，并通过幂律到达示例展示各节点年龄按不同标度增长但仍遵循$O(1)$上界。