Analysis of Random Mobility Models with Partial Differential Equations

In this paper, we revisit two classes of mobility models which are widely used to represent users' mobility in wireless networks: random waypoint (RWP) and random direction (RD). For both models, we obtain systems of partial differential equations which describe the evolution of the users' distribution. For the RD model, we show how the equations can be solved analytically both in the stationary and transient regime, adopting standard mathematical techniques. Our main contributions are 1) simple expressions which relate the transient duration to the model parameters and 2) the definition of a generalized random direction model whose stationary distribution of mobiles in the physical space corresponds to an assigned distribution.