  In this paper, we examine the cause of the border effect 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 diffusion
equation. In particular demonstrate that these conditions are satisfied 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
reflection 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 diffusion equation. We suggest a generalization of the RWP
model that can provide more uniform mobile node distributions.
