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# Ad-hoc Networks: Fundamental Properties and Network by Ramin Hekmat

By Ramin Hekmat

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Extra info for Ad-hoc Networks: Fundamental Properties and Network Topologies

Example text

In each simulation we distribute N nodes over an area of x × y (normalized values). 13) and calculate the degree distribution for all nodes. 4), when the border eﬀect is negligible. The coverage ﬂuctuations do not seem to distort the binomial distribution of the node degree. In the following two paragraphs we elaborate this conclusion. Eﬀect of coverage ﬂuctuations To be able to investigate the eﬀect of coverage ﬂuctuations separate from the border eﬀect, the area can be considered as a torus with toroidal distances between the nodes.

6 Chapter summary In this chapter we described important characteristics of random graphs, lattice graphs, scale-free graphs and the pathloss geometric random graphs to position our model for ad-hoc networks. Our model for ad-hoc networks is based on the medium scale signal power ﬂuctuations in radio communications and assumes that these power ﬂuctuations have a lognormal distribution. We have discussed why our lognormal geometric random graph model can be a realistic way of modeling ad-hoc networks.

This property follows directly from the uniform distribution of nodes and can be veriﬁed easily. 2. This observation implies that degree distribution in an ad-hoc network must be binomial as well, even if the shape of the coverage area of any node may be very irregular. However, in an ad-hoc network there are two factors that make the situation more complex. At the ﬁrst place because the coverage area is determined by a probability function, the coverage area of each node does not have a ﬁxed shape and can vary from node to node.