  We study connectivity properties in a probabilistic model for a large mobile
ad-hoc network. We consider a large number of participants of the system moving
randomly, independently and identically distributed in a large domain, with a
space-dependent population density of finite, positive order and with a fixed
time horizon. Messages are instantly transmitted according to a relay
principle, that is, they are iteratively forwarded from participant to
participant over distances smaller than the communication radius until they
reach the recipient. In mathematical terms, this is a dynamic continuum
percolation model. We consider the connection time of two sample participants,
the amount of time over which these two are connected with each other. In the
above thermodynamic limit, we find that the connectivity induced by the system
can be described in terms of the counterplay of a local, random and a global,
deterministic mechanism, and we give a formula for the limiting behaviour. A
prime example of the movement schemes that we consider is the well-known random
waypoint model. Here, we give a negative upper bound for the decay rate, in the
limit of large time horizons, of the probability of the event that the portion
of the connection time is less than the expectation.
