Traffic jam and discontinuity induced by slowdown in two-stage optimal-velocity model

We study the traffic states and jams induced by a slowdown of vehicles in a single-lane highway. The two-stage optimal velocity model is used in which the optimal velocity function has two turning points. The fundamental (flow-density) diagrams are calculated. At low density, the flow (current) increases linearly with density, while it saturates at some values of intermediate density. When the flow saturates, the discontinuous front (stationary shock wave) appears before or within the section of slowdown. The values of saturated flow are determined by the extreme values of theoretical current curves. The relationship between the densities is derived before and after the discontinuity.