Statistical Characterizers of Transport in a Communication Network

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 logarithmic 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 one-dimensional 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. The distributions are explained using a stochastic differential equation to model the transport.