  We study delay tolerant networking (DTN) and in particular, its capacity to
store, carry and forward messages so that the messages eventually reach their
final destinations. We approach this broad question in the framework of
percolation theory. To this end, we assume an elementary mobility model, where
nodes arrive to an infinite plane according to a Poisson point process, move a
certain distance L, and then depart. In this setting, we characterize the mean
density of nodes required to support DTN style networking. In particular, under
the given assumptions, we show that DTN is feasible when the mean node degree
is greater than 4 e(g), where parameter g=L/d is the ratio of the distance L to
the transmission range d, and e(g) is the critical reduced number density of
tilted cylinders in a directed continuum percolation model. By means of Monte
Carlo simulations, we give numerical values for e(g). The asymptotic behavior
of e(g) when g tends to infinity is also derived from a fluid flow analysis.
