Abstract
In a wireless ad hoc networks where all mobile nodes (MNs) have the same transmission range and the MN density is sufficiently high, the actual hop count between any two MNs is proportional to the distance between them. This paper shows the relation between distance and hop count first. Then, based on the relation, the required hop count between two given MNs is estimated. With the distribution of distance between pairs of MNs, this paper also suggests the optimal transmission power of MNs, which can guarantee delay constraints of a requested ratio of connections in an entire network. All problems are investigated in both a two-dimensional and a three-dimensional area. Simulation results substantiate the accuracy of the proposed approximation methods. The errors of the hop count estimation method are just 0.88% and 2.33% in a 2D and 3D area.
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