  There has been considerable interest in the active maneuvers made by a small
number of vehicles to improve macroscopic traffic flows. Jam-absorption driving
(JAD) is a single vehicle's maneuvers to remove a wide moving jam and consists
of two actions. First, a vehicle upstream of the jam slows down and maintains a
low velocity. Because it cuts off the supply of vehicles to the jam, the jam
shrinks and finally disappears. Second, it returns to following the vehicle
ahead of it. One of the critical problems of JAD is the occurrence of secondary
jams. The perturbations caused by JAD actions may grow into secondary jams due
to the instability of traffic flows. The occurrence of secondary jams was
investigated by numerical simulations in non-periodic systems where only
human-driven vehicles are placed upstream of the vehicle performing JAD.
However, no theoretical condition has been proposed to restrict secondary jams
in these systems. This paper presents a theoretical condition restricting
secondary jams in a semi-infinite system composed of a vehicle performing JAD
and the other human-driven vehicles obeying a car-following model on a
non-periodic and single-lane road. In constructing this condition, we apply the
linear string stability to a macroscopic spatiotemporal structure of JAD.
Numerical simulations show that a finite version of this condition restricts
secondary jams. Moreover, under this condition, we demonstrate that it is
possible to restrict secondary jams in the semi-infinite system under wide
ranges of the parameters of the system. Furthermore, we construct the
conditions suppressing secondary jams in other semi-infinite systems with
inflows from other lanes or a bottleneck, and demonstrate that JAD can restrict
secondary jams in these systems. Thus, our method theoretically guarantees that
a single vehicle can improve macroscopic traffic flows.
