Power Law Models For Connectivity of Random Geometric Graphs
Abstract
This paper addresses the connectivity properties of ad hoc wireless networks. These networks do not rely on a fixed infrastructure to make up for the limited communication range of nodes, but instead achieve connectivity through cooperative, peer-to-peer, multi-hop routing. Ad hoc wireless networks can be used for intra-team communications by military personnel or first responders, ground-based vehicle networks, airborne networks, and even provide device-to-device communication without cell towers. Networks composed of nodes with fixed communication range can be modeled as Random Geometric Graphs (RGGs). Modeling the connectivity properties of these networks is critical to evaluating their performance as well as their vulnerability to failure or attack. Knowledge of these properties can also improve survivability by ensuring that the network is not fully connected, such as to mitigate the transmission of disease or malware. RGGs are modeled in flat and toroidal square spaces as well as in circles and rectangular spaces of various aspect ratios. They are modeled in spaces without obstructions, in spaces with regularly and randomly placed obstructions, and in lattices. RGGs are modeled largely in two-dimensional spaces but also in spaces of dimensions one through six. Two RGG growth models are considered, where a given connectivity goal is achieved either by adding nodes with fixed communication range or by finding the minimum necessary range of a fixed set of nodes. Regression analysis is applied to the outputs of simulations of RGG growth to obtain expressions that predict various statistical metrics for full connectivity, partial connectivity, and no isolated nodes. It is shown that power law (log-log) models yield accurate statistical metrics for these forms of connectivity for both growth models, although log law models performed slightly better for square lattices. The accuracies of inverse regression and reverse regression were tested.
Document Details
- Document Type
- Technical Report
- Publication Date
- Dec 01, 2022
- Accession Number
- AD1187085
Entities
People
- Mark H. Linderman
- Warren H. Jr Debany
Organizations
- Rome Laboratory