Results on Finite Wireless Networks on a Line

Abstract— Today, due to the vast amount of literature on largescale wireless networks, we have a fair understanding of the asymptotic behavior of such networks. However, in real world we have to face finite networks for which the asymptotic results cease to be valid. We refer to networks as being finite when the number of nodes is less than a few hundred. Here we study a model of wireless networks, represented by random geometric graphs. In order to address a wide class of the network’s properties, we study the threshold phenomena. Being extensively studied in the asymptotic case, the threshold phenomena occurs when a graph theoretic property (such as connectivity) of the network experiences rapid changes over a specific interval of the underlying parameter. Here, we find an upper bound for the threshold width of finite line networks represented by random geometric graphs. These bounds hold for all monotone properties of such networks. We then turn our attention to an importan...

• Type: Journal
• Year: 2010
• Where: TCOM
• Authors: Ali Eslami, Mohammad Nekoui, Hossein Pishro-Nik
• Keywords: Random Geometric Graphs, TCOM 2010, Threshold Phenomena, Wireless Networks