Stochastic Geometry for Wireless Networks
Random geometric graphs have provided an excellent framework for modeling in wireless networks. Vertices of the graphs form the communicating entities and an edge between two nodes in the graph indicates the ability of the two nodes to communicate. In the simplest model, two edges are connected if the distance between the two nodes is less than a cutoff radius. Our interest is in the behavior of the system when the number of nodes is large. First we will discuss some point process models for describing the distribution of the nodes, and derive some properties of the Poisson point process. Then the problems of coverage, percolation and connectivity will be discussed. These include the radius required to cover an arbitrary fraction of the space, existence of a phase transition or the emergence of a giant component and the critical radius required for the graph to be connected with high probability.