Stochastic properties of the random waypoint mobility model

The random waypoint model is a commonly used mobility model for simulations of wireless communication networks. By giving a formal description of this model in terms of a discrete-time stochastic process, we investigate some of its fundamental stochastic properties with respect to: ( a) the transition length and time of a mobile node between two waypoints, (b) the spatial distribution of nodes, ( c) the direction angle at the beginning of a movement transition, and (d) the cell change rate if the model is used in a cellular-structured system area. The results of this paper are of practical value for performance analysis of mobile networks and give a deeper understanding of the behavior of this mobility model. Such understanding is necessary to avoid misinterpretation of simulation results. The movement duration and the cell change rate enable us to make a statement about the "degree of mobility" of a certain simulation scenario. Knowledge of the spatial node distribution is essential for all investigations in which the relative location of the mobile nodes is important. Finally, the direction distribution explains in an analytical manner the effect that nodes tend to move back to the middle of the system area.