A Geometry Study on the Capacity of Wireless Networks Via Percolation
In this paper, the authors investigate the impact of the geometry on the percolation and the capacity among different network models. In a strip network, the achievable rate is restricted by the maximum length of the sides in the supercritical scenario. And in the subcritical scenario, the authors figure out that the capacity will degenerate to that of a 1D network in a step-by-step manner. Similar phenomena are found in a triangle network and 3D networks as well. The transmission rate of nodes in the corner of a triangle network can be a bottleneck for the whole network. In a cuboid network, percolation highway disappears when the length of the other edges are "Too small" compared with the maximum length of the edges.