Message transport characteristics in communication networks

We study message transport on a $1-d$ ring of nodes and randomly distributed hubs. Messages are deposited on the network at a constant rate. When the rate at which messages are deposited on the lattice is very high, messages start accumulating after a critical time and the average load per node starts increasing. The power-spectrum of the load time-series shows $1/f$ like noise similar to the scenario of the Internet traffic. The inter-arrival time distribution of messages for the $1-d$ ring network shows stretched exponential behavior, which crosses over to power-law behavior if assortative connections are added to the hubs. The distribution of travel times in a related double ring geometry is shown to be bimodal with one peak corresponding to initial congestion and another peak to later decongestion.