Age of Information in Multihop Multicast Networks

We consider the age of information in a multihop multicast network where there is a single source node sending time-sensitive updates to $n^L$ end nodes, and $L$ denotes the number of hops. In the first hop, the source node sends updates to $n$ first-hop receiver nodes, and in the second hop each first-hop receiver node relays the update packets that it has received to $n$ further users that are connected to it. This network architecture continues in further hops such that each receiver node in hop $\ell$ is connected to $n$ further receiver nodes in hop $\ell+1$. 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 in each hop, 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 $n$ first-hop nodes, and each first-hop node that receives the update relays it to the earliest $k_2$ out of $n$ second-hop nodes that are connected to it and so on. We determine the optimum $k_\ell$ stopping value for each hop $\ell$ for arbitrary shifted exponential link delays.