  We consider Markov models of large-scale networks where nodes are
characterized by their local behavior and by a mobility model over a
two-dimensional lattice. By assuming random walk, we prove convergence to a
system of partial differential equations (PDEs) whose size depends neither on
the lattice size nor on the population of nodes. This provides a macroscopic
view of the model which approximates discrete stochastic movements with
continuous deterministic diffusions. We illustrate the practical applicability
of this result by modeling a network of mobile nodes with on/off behavior
performing file transfers with connectivity to 802.11 access points. By means
of an empirical validation against discrete-event simulation we show high
quality of the PDE approximation even for low populations and coarse lattices.
In addition, we confirm the computational advantage in using the PDE limit over
a traditional ordinary differential equation limit where the lattice is modeled
discretely, yielding speed-ups of up to two orders of magnitude.
