  We study message transfer in a $2-d$ communication network of regular nodes
and randomly distributed hubs. We study both single message transfer and
multiple message transfer on the lattice. The average travel time for single
messages travelling between source and target pairs of fixed separations shows
$q-$exponential behaviour as a function of hub density with a characteristic
power-law tail, indicating a rapid drop in the average travel time as a
function of hub density. This power-law tail arises as a consequence of the
log-normal distribution of travel times seen at high hub densities. When many
messages travel on the lattice, a congestion-decongestion transition can be
seen. The waiting times of messages in the congested phase show a Gaussian
distribution, whereas the decongested phase shows a log-normal distribution.
Thus, the congested or decongested behaviour is encrypted in the behaviour of
the waiting time distributions.
