Vehicle flow and phase transitions in traffic networks

A computer simulation of a simple dynamical model of vehicles moving across a two-dimensional traffic network is performed. Traffic management is enforced through the roundabouts: providing the conditions are appropriate, vehicles can move through the roundabouts. When the density of the travelling traffic is low, the vehicles can move freely. Increasing the vehicle density leads to structured patterns which initially enable a high density of vehicles to travel throughout the system but eventually leads to gridlock. A phase transition separates a congestion free phase from a congested one as the vehicle density increases.