Analysis of the Robustness Dynamics of Wireless Mobile Ad Hoc Networks via Time Varying Dual Basis Representation

Abstract

Many network models are too complex to readily identify which structural aspects of a network are most influential on robustness. To analyze the dynamics and robustness of a network, many of the protocol details can be reduced to a graph theory representation of nodes, links and link weights. Our method uses the spectral analysis of the Laplacian matrix to decouple the interactions between nodes to analyze the robustness of a wireless mobile ad hoc network (MANET) with a time-varying wireless channel. This spectral analysis and the resulting algebraic connectivity can be used to determine how robust a network is, where the weak links are, and how to best increase overall performance of a network. Using a simulation of wireless devices in a MANET with a time- varying channel, we show that robustness is a function of time, that nodes become coupled and decoupled as the structure of the network changes and that any robustness analysis is more complete when more than a single eigenvalue is evaluated.