A microscopic derivation of a traffic flow model on a junction with two entry lines

We derive a conservation law on a network made of two incoming branches and a single outgoing one from a discrete traffic flow model. The continuous model is obtained from the discrete one by letting the number of vehicles tend to infinity and after scaling. In the discrete model, the vehicles solve a follow-the-leader model on each branch. The priority rule at the junction is given by a time-periodic traffic light (with – for technical reasons – a period tending to infinity with the scaling). The conservation law at the limit is L 1 -contractive and described in terms of a germ depending on the flux and on the average amount of time the traffic light is “green” on a branch.