We consider a Jackson-type network, each of whose nodes contains
N identical channels with a single server. Upon arriving at a node, a
task selects m of the channels at random and joins the shortest of the
m queues observed.We fix a collection of channels in the network, and
analyze how the queue-length processes at these channels vary as $N \to
\infty$. If the initial conditions converge suitably, the distribution of these
processes converges in local variation distance to a limit under which each
channel evolves independently.We discuss the limiting processes which arise,
and in particular we investigate the point processes of arrivals and departures
at a channel when the networks are in equilibrium, for various values of the
system parameters.