Abstract
In a wireless ad hoc network, messages are transmitted, received, and forwarded in a finite geometrical region and the transmission of messages is highly dependent on the locations of the nodes. Therefore the study of geometrical relationship between nodes in wireless ad hoc networks is of fundamental importance in the network architecture design and performance evaluation. However, most previous works concentrated on the networks deployed in the two-dimensional region or in the infinite three-dimensional space, while in many cases wireless ad hoc networks are deployed in the finite three-dimensional space. In this paper, we analyze the geometrical characteristics of the three-dimensional wireless ad hoc network in a finite space in the framework of random graph and deduce an expression to calculate the distance probability distribution between network nodes that are independently and uniformly distributed in a finite cuboid space. Based on the theoretical result, we present some meaningful results on the finite three-dimensional network performance, including the node degree and the max-flow capacity. Furthermore, we investigate some approximation properties of the distance probability distribution function derived in the paper.
Highlights
A wireless ad hoc network can be considered as one consisting of a collection of nodes, and the relationship between them is peer to peer
For networks in the infinite two-dimensional region, based on the inverse power law model of attenuation with lognormal shadowing fading, Orriss and Barton [6] proved that the number of audible stations of a station, corresponding to the node degree in this paper, obeys the Poisson distribution
For a wireless ad hoc network in the finite two-dimensional region, we presented, in [5], that the probability distribution of node degree is much more complicated, even in the absence of random shadowing
Summary
A wireless ad hoc network can be considered as one consisting of a collection of nodes, and the relationship between them is peer to peer. For networks in the infinite two-dimensional region, based on the inverse power law model of attenuation with lognormal shadowing fading, Orriss and Barton [6] proved that the number of audible stations of a station, corresponding to the node degree in this paper, obeys the Poisson distribution This comprehends the special case of random graph model above, which does not allow random shadowing. In this paper, based on the random graph model, we will present further results on the max-flow capacity of the three-dimensional networks in a finite space, under the assumption that each link has unit capacity.
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