Analytical Bounds on the Critical Density for Percolation in Wireless Multi-hop Networks
In this paper we develop analytical bounds on the critical density for percolation in wireless multi-hop networks, but in contrast to other studies, under a random connection model and with nodes Poissonly distributed in the plane R2. The establishment of a direct connection between any two nodes follows a random connection model satisfying some intuitively reasonable conditions, i.e. rotational and translational invariance, non-increasing monotonicity and integral boundedness. It is well known that under the above network model and connection model there exists a critical density below which almost surely a fixed but arbitrary node is connected (via single or multi-hop path) to finite number of other nodes only, and above which the node is connected to an infinite number of other nodes with a positive probability. In this paper we investigate the bounds on the critical density. The result is compared with the existing results under a specific connection model, i.e. the unit disk communication model, and it is shown that our method generates bounds close to the known ones. The result provides valuable insight into the design of large-scale wireless multi-hop networks.
Keywords: random geometric graph, critical density, Poisson random connection model, percolation