We study the connectivity properties of an ad hoc network consisting of n nodes each moving according to the Random Waypoint mobility model. In particular, we focus on estimating two quantities, the probability that the network is connected, and the mean durations of the connectivity periods. The accuracy of the approximations is compared against numerical simulations. For the probability of connectivity, an approximation is given that is remarkably accurate. By numerical examples we also show that in sparse network the mobility has a positive effect on connectivity, whereas in dense network the situation becomes the opposite. For the mean length of the connectivity periods results are also accurate in the important region where the probability of connectivity rises rapidly.

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In previous work, the effects of randomized beamforming, i.e., the strategy of every node in a wireless multihop network directing its antenna in a randomly chosen direction, on connectivity are studied by simulation. In this paper, we study some such effects analytically under similar but slightly simplified modeling assumptions. We begin by generalizing the notion of the threshold range for k-connectivity from the traditional Boolean network model to networks with arbitrary link attenuations. Then, for a network of uniformly distributed nodes with randomized beamforming, we derive analytically and evaluate numerically the degree distribution of a random node. Based on this, we apply a commonly used approximation to the probability that such a network is k-connected.We find that because the randomness caused by this strategy in the link attenuations shifts the network topology from being strictly a geometric random graph towards being a pure random graph, the k-connectivity probability of a network applying randomized beamforming can be approximated more accurately than that of a network with omnidirectional antennas. This added randomness also manifests itself as the increased variance of the node degree and the threshold attenuation range for k-connectivity. The main conclusion from our findings is that randomized beamforming cannot be said to strictly improve -nor to degrade -the connectivity of random wireless multihop networks.