Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Wireless Communications: Principles and Practice
Wireless Communications: Principles and Practice
Topological Characteristics of Random Multihop Wireless Networks
ICDCSW '03 Proceedings of the 23rd International Conference on Distributed Computing Systems
IEEE Transactions on Wireless Communications
The capacity of wireless networks
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
IEEE Transactions on Information Theory
CAAN'06 Proceedings of the Third international conference on Combinatorial and Algorithmic Aspects of Networking
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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.