The Limit of Information Propagation Speed in Large-Scale Multihop Wireless Networks

This paper investigates the speed limit of information propagation in large-scale multihop wireless networks, which provides fundamental understanding of the fastest information transportation and delivery that a wireless network is able to accommodate. We show that there exists a unified speed upper bound for broadcast and unicast communications in large-scale wireless networks. When network connectivity is considered, this speed bound is a function of node density. If the network noise is constant, the bound is a constant when node density exceeds a threshold; if the network noise is an increasing function of node density, the bound decreases to zero when node density approaches infinity. As achieving the speed bound places strict requirements on node locations, we also quantify the gap between the actual achieved speed and the desired bound in random networks in which the relay nodes are not located as desired. We find that the gap converges to zero exponentially as node density increases to infinity.