An Analytical Model for the Node Degree in Wireless Ad Hoc Networks

Node degree is regarded as an important and convenient metric to measure the connectivity of wireless ad hoc networks. Existing studies are mainly based on the assumption that nodes are static and do not provide closed-form expressions for node degree. In this paper, we investigate three fundamental characteristics of a wireless ad hoc network: Its node degree distribution, its average node degree and its maximum node degree experienced by the nodes during their movement. We introduce a novel mathematical model to derive analytical expressions in the presence of radio channel fading. Furthermore, our results reveal that the node degree distribution follows a binomial distribution regardless of the initial distribution of nodes’ location. The results of this paper are useful to study node connectivity and to improve the algorithmic complexity of incentive protocols.

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