An analysis of the node spatial distribution of the random waypoint mobility model for ad hoc networks

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Abstract
In this paper we analyze the node spatial distribution generated by nodes moving according to the random waypoint model, which is widely used in the simulation of mobile ad hoc networks. We extend an existing analysis for the case in which nodes are continuously moving (i.e., the pause time is 0) to the more general case in which nodes have arbitrary pause times between movements. We also generalize the mobility model, allowing the nodes to remain stationary for the entire simulation time with a given probabilit . Our analysis shows that the structure of the resulting as asymptotic spatial density is composed by three distinct components: the initial, the pause and the mobilit component. The relative values of these components depend on the mobilit parameters. We derive an explicit formula of the one-dimensional node spatial density, and an approximated formula for the two-dimensional case.The quality of this approximation is verified through experimentation, which shows that the accuracy heavily depends on the choice of the mobilit parameters.

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