  We identify the statistical characterizers of congestion and decongestion for
message transport in model communication lattices. These turn out to be the
travel time distributions, which are Gaussian in the congested phase, and
log-normal in the decongested phase. Our results are demonstrated for two
dimensional lattices, such the Waxman graph, and for lattices with local
clustering and geographic separations, gradient connections, as well as for a
1-d ring lattice with random assortative connections. The behavior of the
distribution identifies the congested and decongested phase correctly for these
distinct network topologies and decongestion strategies. The waiting time
distributions of the systems also show identical signatures of the congested
and decongested phases.
