Connectivity Properties of Random Waypoint Mobility Model for Ad Hoc Networks

We study the connectivity properties of an ad hoc network consisting of a given number of nodes each moving according to the Random Waypoint mobility model. Connectivity properties of networks with uniformly distributed nodes are well known, but the movement in the RWP model results in a spatial node distribution which is not uniform. Approximations are provided for the probability that the network is connected, as well as for the mean durations of the connectivity periods. The accuracy of the approximations is compared against extensive numerical simulations. Especially, for the probability of connectivity, based on new results on the exact node location distribution, an approximation is given that is remarkably accurate. Furthermore, it is shown by numerical examples 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 an approximation is derived that gives accurate results in the important region where the probability of connectivity rises rapidly.