Analyzing Finite MANETs by Transformations to Equivalent Static Graphs

Because of their importance in military and other applications, Mobile Ad-Hoc Wireless Networks or MANETs have attracted significant attention in the research community. However, almost virtually all of the literature has focused on analyzing MANETs in an asymptotic case with a very large number of nodes under varying assumptions on node density and distribution. While the asymptotic analysis is extremely valuable, practical usage of MANETs requires us to be able to analyze networks of finite size. In this paper, we present an approach to analyze MANETs with a fixed number of nodes which can be used in many practical applications related to MANETs. Our approach is based on simplifying the motion paths of MANETs by applying a set of transformations, and decomposing the motion paths into a generalized Fourier series transformation of simpler periodic motions.