Age of Information in Multihop Multicast Networks
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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 ℓ is connected to n further receiver nodes in hop ℓ+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_ℓ stopping value for each hop ℓ for arbitrary shifted exponential link delays.
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