Fundamental traffic diagrams of elementary road networks

The fundamental traffic diagram gives the relation between the flow and the density of vehicles on a road. This diagram has been obtained for one circular road in the deterministic and stochastic cases. In this paper we revisit the simplest example of two roads and one crossing given in [2] and we study the interaction between crossings on a system of four roads with two crossings. After showing numerically the existence of an average flow, we compute the fundamental diagram of the system and we study its various phases. We compare the fundamental diagrams obtained with different crossing policies (right priority, open-loop and feedback traffic light). We show that the “right priority” policy blocks the system at a specific vehicle density. This jam is explained by the appearance of a road circuit full of vehicles. Finally we show the important influence of the crossing design on the fundamental diagram.