Modeling Synchronized Flow at Highway Bottlenecks

Summary

Many experimental studies have shown the appearance of synchronized flow at highway bottlenecks. We study highway bottlenecks within the macroscopic BVT model. The BVT model describes traffic flow as a hyperbolic system of balance laws. It generalizes the traffic model of Aw, Rascle and Greenberg by introducing in the momentum equation a new source term, which can become negative due to the finite reaction and relaxation times of drivers. The model is capable of reproducing multivalued fundamental diagrams, the metastability of free traffic flow at the onset of instabilities and wide moving jams. Based on previous work we describe the coupling conditions for the Riemann problem of the system and apply them to highway bottlenecks. We focus our study on the situation where the bottlenecks are either caused by the reduction of the number of lanes or by on-ramps or off-ramps. Our numerical simulations reproduce the appearance of synchronized flow at these highway bottlenecks. The analysis of the lane reduction setup shows that the outflow from the synchronized flow region in front of the bottleneck is constant and below the maximum free flow. This observation can be understood from the study of the static solutions within the model. As a consequence of the coupling conditions static solutions have to cross the jam line, one of the additional equilibrium solutions within the BVT model. This crossing determines the flow value of the static solution.