Age-Aware Gossiping in Network Topologies

Purbesh Mitra, Sennur Ulukus

Abstract: 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 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 show that this $O(1)$ age performance is sustained if a network has only a fraction of fully-connected edges. However, if the nodes have finite $O(1)$ connectivity, e.g., ring networks, two-dimensional grids, we show that ASUMAN scheme underperforms uniform gossiping, pointing to the need for connectivity with opportunistic gossiping. We improve this performance by introducing a hierarchical structure in the network, which recovers $O(1)$ age scaling under $O(\sqrt {n})$ connected networks. Further, we show how the age of the nodes scale when the cluster heads are finitely connected among themselves, e.g., $O(c)$ age scaling for disconnected and $O(\sqrt {c})$ age scaling for ring-connected cluster heads, where c is the number of clusters. 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.

External IDs:doi:10.1109/tcomm.2024.3397806