Theory of jam-absorption driving

“Can a single car really absorb a traffic jam without making new jams?” In this paper, we focus on this frequently-discussed question, and have succeeded in making a theoretical framework of a driving technique how to absorb a traffic jam by using a minimal microscopic model. Jam-absorption driving comes from Beaty (Beaty, 1998, Beaty, 2013), and it is composed of a sequence of two actions termed the “slow-in” and “fast-out”. The “slow-in” is the action to avoid being captured by a jam and remove it by decelerating and taking a longer headway in advance. The “fast-out” is performed after the “slow-in”, and it is the action to follow the car in front without unnecessary time gaps by accelerating quickly. In our theoretical framework, we have represented the recipe of the actions such as the time–space points and the velocity. Moreover, we have clarified the condition of no secondary jams due to this driving, i.e., the condition that compression and expansion waves caused by this driving meet each other and disappear. Particularly, we have calculated how these waves propagates to the following cars and the point where and when they disappear. Besides, we have analyzed how this point moves in time–space diagrams by varying the timing to start the jam-absorption, and revealed that the pattern of this movement is not constant but changes greatly by the velocity-headway relationships. Furthermore, as a more realistic problem, we have formulated the driving for jam-absorption in two steps of deceleration, which brings rich patterns of collisions among compression and expansion waves.