Instability of a traffic jam induced by slowing down

A traffic jam induced by slowing down is investigated using the optimal velocity model of the car following models, When cars are decelerated in the presence of hindrances, two kinds of traffic jam occur behind the hindrance: one is an oscillating jam and the other ia a homogeneous jam. When the slowing down is small, the oscillating jam occurs. If the slowing down is large, the jam is homogeneous our space and time. The linear stability theory is applied to the traffic jam. The critical line and critical mode of the instability are found. It is shown that the boundary between the oscillating and homogeneous jams is consistent with the critical line of the linear stability. The periods of the oscillating jam are about two times and four times the critical mode estimated by the linear stability theory.