Asymptotic Distribution of Isolated Nodes in Secure Wireless Sensor Networks under Transmission Constraints

Abstract

The Eschenauer-Gligor (EG) key predistribution is regarded as a typical approach to secure communication in wireless sensor networks (WSNs). In this paper, we establish asymptotic results about the distribution of isolated nodes and the vanishing small impact of the boundary effect on the number of isolated nodes in WSNs with the EG scheme under transmission constraints. In such networks, nodes are distributed either Poissonly or uniformly over a unit square. The results reported here strengthen recent work by Yi et al.