A Sparse Clustering Model of Wireless Communication Networks

This paper gives results on the use of stochastic geometry with small cluster for the performance analysis of large wireless networks. The aim is to present a generalization of the assertion that a point process on a wireless communication network significantly depends on the links. In real world graph constructions, the decision on whether to connect two nearby points depends not only on the distance between the nearby points but also on the interaction between them. Motivated by the attempt to unify systematic development and application in modeling real world networks, we propose a new model, called related point process, to generate a random graph and point process by a two-step procedure: 1) the generation of a point process, and 2) the application of a kernel family to each edge to produce sub graphs. It is an alternative approach to specifying a structure of a small cluster in a wireless communication network. We also consider some properties of the model, showing, for example, the degree distribution by using a probability generating functional and giving some asymptotic analysis of the sub graph count. In particular, although our main concern is the power law distribution, we also take into account cases where the distribution model is arbitrary.