On the Geometrical Characteristic of Wireless Ad-Hoc Networks and its Application in Network Performance Analysis

A wireless ad-hoc network can be roughly considered as one consisting of a collection of mobile nodes distributed in a finite region, which adopts a non-centralized and self-organized structure. In such networks, messages are transmitted, received and forwarded in a finite geometrical region. In addition, the transmission of messages is highly dependent on the locations of the mobile nodes. As a result, the geometrical relationships between the nodes, and especially the distance between them are of fundamental importance. In this paper, we propose a space decomposition method to analyze the probability distribution of the distance between nodes in an ad-hoc network. In particular, we derive two theoretical expressions for the probability distribution of the distance between nodes under the assumption that the nodes are independently and uniformly distributed in either a rectangular region or hexagonal region. Further results on the node degree distribution and max-flow capacity of the network are then presented based upon these expressions