Spatial Node Distribution of Manhattan Path Based Random Waypoint Mobility Models with Applications

In this paper, we study the spatial node stationary distribution of two variations of the Random Waypoint (in short, RWP) mobility model. In particular, differently from the RWP mobility model, that connects source to destination points by straight lines, our models make use of Manhattan or (more realistically) Bezier paths. We provide analytical results for the spatial node stationary distribution for the two Manhattan based RWP mobility models and experimental evidence that the Bezier based models do not significantly differ from the Manhattan ones. This implies that Manhattan based RWP models can be considered a good approximation of the more realistic Bezier ones. As a case study, we exploit our results about one of the two Manhattan based RWP models to derive an upper bound on the transmission range of the nodes of a MANET, moving according to this model, that with high probability guarantees the connectivity of the communication graph.