Large Network Models and Their Implications

Abstract

Connectivity of large wireless networks has been a primary concern for which asymptotic analysis is a useful tool. Three related but logically distinct network models are often considered in asymptotic analyses, viz., the dense network model, the extended network model, and the infinite network model, which considers respectively a network deployed in a fixed finite area with a sufficiently large node density, a network deployed in a sufficiently large area with a fixed node density, and a network deployed in an infinite plane with a sufficiently large node density. The infinite network model originated from continuum percolation theory and asymptotic results obtained from the infinite network model have often been applied to the dense and extended networks indiscriminately. In this chapter, through two case studies related to network connectivity on the expected number of isolated nodes and on the vanishing of components of finite order k > 1 respectively, we demonstrate some subtle but important differences between the infinite network model and the dense and extended network models. Therefore, extra scrutiny has to be used in order for the results obtained from the infinite network model to be applicable to the dense and extended network models. Asymptotic results are also established on the expected number of isolated nodes, the vanishingly small impact of the boundary effect on the number of isolated nodes and the vanishing of components of finite order k > 1 in the dense and extended network models using a general random connection model.