Article

# Connectivity of a Gaussian network

University of Cambridge, CB2 1TQ, Cambridge, UK

International Journal of Ad Hoc and Ubiquitous Computing (Impact Factor: 0.55). 01/2008; 3(3):204-213. DOI: 10.1504/IJAHUC.2008.018407 Source: DBLP

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**ABSTRACT:**In this review paper, we shall discuss some recent results concerning several models of random geometric graphs, including the Gilbert disc model G r , the k-nearest neighbour model G k nn and the Voronoi model G P . Many of the results concern finite versions of these models. In passing, we shall mention some of the applications to engineering and biology.05/2010: pages 117-142; - [Show abstract] [Hide abstract]

**ABSTRACT:**Wireless sensor networks (WSNs) consist of thousands of nodes that need to communicate with each other. However, it is possible that some nodes are isolated from other nodes due to limited communication range. This paper focuses on the influence of communication range on the probability that all nodes are connected under two conditions, respectively: (1) all nodes have the same communication range, and (2) communication range of each node is a random variable. In the former case, this work proves that, for , if the probability of the network being connected is , by means of increasing communication range by constant , the probability of network being connected is at least . Explicit function is given. It turns out that, once the network is connected, it also makes the WSNs resilient against nodes failure. In the latter case, this paper proposes that the network connection probability is modeled as Cox process. The change of network connection probability with respect to distribution parameters and resilience performance is presented. Finally, a method to decide the distribution parameters of node communication range in order to satisfy a given network connection probability is developed.International Journal of Distributed Sensor Networks 09/2013; 2013(2). DOI:10.1155/2013/482727 · 0.67 Impact Factor - International Journal of Distributed Sensor Networks 04/2014; Volume 2014(2014). DOI:10.1155/2014/370512 · 0.67 Impact Factor