Phase transition in a directed traffic flow network

Abstract

The generic feature of traffic in a network of flowing electronic data packets is a phase transition from a stationary free-flow phase to a continuously growing congested nonstationary phase. In the most simple network of directed oriented square lattice we have been able to observe all crucial features of such flow systems having nontrivial critical behavior near the critical point of transition. The network here is in the shape of a square lattice and data packets are randomly posted with a rate rho at one side of the lattice. Each packet executes a directed diffusive motion toward the opposite boundary where it is delivered. Packets accumulated at a particular node form a queue and a maximum of m such packets randomly jump out of this node at every time step to its neighbors on a first-in-first-out basis. The phase transition occurs at rho(c) = m. The distribution of travel times through the system is found to have a log-normal behavior and the power spectrum of the load time series shows 1/f-like noise similar to the scenario of Internet traffic.