A behavioral theory of multi-lane traffic flow. Part II: Merges and the onset of congestion

This paper examines the behavior of multi-lane freeway traffic past on-ramps, building on the continuum model of part I and focusing on the onset of congestion. The main complication is that rabbits (fast vehicles) entering from an on-ramp usually stay on the shoulder lane(s) of the freeway for some distance before merging into the fast lane(s). An idealization is proposed, where this distance is taken to be the same for all vehicles. As a result, the system behaves as if there was a fixed buffer zone downstream of the on-ramp where entering rabbits cannot change lanes. The model of part I is extended to capture the peculiarities of traffic within such a buffer zone, including its two end-points: the "entrance" and the "merge". The onset of congestion is described by means of waves. The paper shows that this highly idealized model (and its more realistic cousins) explains qualitatively all the puzzling facts discussed in part I without introducing obviously unreasonable phenomena. A typical sequence of events during the onset of congestion is predicted to be as follows: (i) increased on-ramp flows and the ensuing merging maneuvers into the median (passing) lane generate a (fast-moving) queue at the merge that grows on the median lane(s) of the buffer; (ii) when the speed in this queue drops below the level on the shoulder lanes, a 1-pipe queue forms at the merge, which then grows upstream across all lanes; (iii) if the front of this queue moves slowly forward, as per the model of part I, then the lane-flows at the merge would be at "capacity" from then on (with roughly the same speed across all lanes) but downstream of the front there would be a "discharge state" with less total flow. Therefore, an observer downstream of the merge would see this discharge state before the capacity state, and would record a drop in flow followed by a recovery. If the front of the queue would move slowly backward, then the sequence of events following (ii) is somewhat different.