Phase Transitions in a Model of Internet Traffic

In a recent study, Ohira and Sawatari presented a simple model of computer network traffic dynamics. These authors showed that a phase transition point is present separating the low-traffic phase with no congestion from the congestion phase as the packet creation rate increases. We further investigate this model by relaxing the network topology using a random location of routers. It is shown that the model exhibits nontrivial scaling properties close to the critical point, which reproduce some of the observed real Internet features. At criticality the net shows maximum information tranfer and efficiency. It is shown that some of the key properties of this model are shared by highway traffic models, as previously conjectured by some authors. The relevance to Internet dynamics and to the performance of parallel arrays of processors is discussed.