Results on Finite Wireless Networks on a Line

13 years 2 months ago

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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...

Ali Eslami, Mohammad Nekoui, Hossein Pishro-Nik

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