Realistic Boundary Conditions for Ad Hoc Network Node Mobility Models and a New Approach to the Random Waypoint Model

In this paper, we examine the cause of the border e ect observed in many mobility models used to construct simulations of ad hoc networking protocol performance. We specify conditions under which a node mobility model must produce spatial mobile node distribution functions that obey the di usion equation. In particular demonstrate that these conditions are satis ed by the random direction (RD) model. We show that it is possible to construct mobility models that attain uniform steady-state distributions without resorting to re ection or \wrapping" of nodes at the border of a test region. Finally, we show that the random waypoint (RWP) model may be reproduced by the application of a \volume rule" to an RD model. This volume rule violates the assumptions that lead to the di usion equation. We suggest a generalization of the RWP model that can provide more uniform mobile node distributions.