Connectivity Analysis For A Wireless Sensor Network Based On Percolation Theory

Connectivity is a key problem in the design of the wireless sensor network. It is also an important indicator for the quality of connectivity and survive in the wireless sensor network ,which is the basic guarantee for the normal operation of the network. In this paper, it studies connectivity in wireless sensor networks based on percolation theoryThe paper presents connectivity problems of wireless sensor network in mathematic -al description. It introduces the basic theory of percolation and its application status in wireless sensor network. For the characteristics which is the large-scale wireless sensor network and the random in the node location and connection between nodes, the connection behavior is described of the percolation phenomenon in the wireless sensor network . Moreover, this paper establish percolation model in the connectivity problem.The wireless sensor network will be divided into dense networks and extend networks of two types in this paper. The number of nodes is analyzed by continuum percolation theory in the connected components of large-scale network. The connectivity is analyzed by bond percolation theory in the connected components of large-scale network. Then, the ratio of the damaged nodes number is studied by simulation, which analysis results provides a better basis for the development of the wireless sensor network.This article also discusses how to analyze connectivity problems of wireless sensor network based on face percolation. The paper first prove that the conditions which percolation occurs. Then, according to regular hexagon, Reuleaux triangle area and face percolation theoretical the analysis of Reuleaux geometric triangle connectivity is more accurate.