Age of Information in Two-Hop Multicast Networks

We consider the age of information in a two-hop multicast network where there is a single source node sending time-sensitive updates to $n^{2}$ end nodes through n middle nodes. In the first hop, the source node sends updates to n middle nodes, and in the second hop each middle node relays the update packets that it receives to n end users that are connected to it. We study the age of information experienced by the end nodes, and in particular, its scaling as a function of n. We show that, using an earliest k transmission scheme, the age of information at the end nodes can be made a constant independent of n. In particular, the source node transmits each update packet to the earliest $k_{1}$ of the n middle nodes, and each middle node that receives the update relays it to the earliest $k_{2}$ out of n end nodes that are connected to it. We determine the optimum $k_{1}$ and $k_{2}$ stopping values for arbitrary shifted exponential link delays.