Authors: Carmine De Nicola, Rosanna Manzo, Vincenzo Moccia, Vincenza Tufano
The aim of this paper is to simulate the effect of traffic lights and time-varying flows distribution at junctions of urban traffic networks. We consider a macroscopic model for road networks based on conservation law, describing the motion of cars as a continuous flow. At junctions some Riemann solvers to find a unique solution to Riemann problems are introduced. In particular we propose a micro-algorithm to define a Riemann solver in situations in which a road in some time-instant is empty and the corresponding problem can be under-determined. Then, we discuss the correct use of Riemann solvers to capture the presence of traffic lights and time-varying behavior of drivers at junctions. Simulation results for a 2 2× junction and a comparison among the effects of changing traffic lights cycles in a network are shown.