Discontinuity at edge of traffic jam induced by slowdown

We study the traffic states and jams induced by a slowdown of vehicles in a single lane highway. We use an extended one of the optimal velocity model to take into account the slowdown in a section of highway. The fundamental (flow-density) diagram is calculated. The flow (current) increases linearly with density, saturates at a critical density, and then decreases with density. When the flow saturates, the discontinuous front (stationary shock wave) appears at the end of traffic jam which begins just before the section of slowdown. The position of discontinuous front moves to the upstream with increasing density. It is found that the relationship between the densities holds before and after the discontinuity, while the flow (current) keeps the saturated value. The region map of distinct jams is shown.