Understanding Congestion

The discharge rate of lane-drop bottlenecks

What to look for: When the simulation starts, the inflow is on the verge of saturation. It increases slightly at t = 2.5 minutes. This quickly triggers a queue on the shoulder lane, forcing vehicles to merge at slower speeds and encouraging mainline vehicles to change lanes.  These lane changes alter the character of traffic through the bottleneck.  They increase density and the ensuing lane changes create voids that cause the bottleneck discharge rate to drop by around 10%.  You can see this by the nearly simultaneous changes in slope of the bottom 2 cumulative curves (for locations x2 and x3, downstream of the bottleneck).  Note as well that at the same time (t = 2.5) the number of lane changes begins to increase at a greater rate and the flow-density diagram at x2 exhibits lower flows at roughly the same “optimal” density. All these phenomena agree rather well with the empirical observations of bottlenecks in Bertini and Leal (2004) and Cassidy and Rudjanakanoknad (2004).  Around t = 5, as the back of the queue recedes over detector x1, the cumulative curve for this detector drops and the drop in flow is also recorded on the corresponding scatter-plot. In this case, though, the density jumps to a higher value signifying that traffic has transitioned into the queued (congested) state.  This again, is in agreement with empirical observation. Note too, how blocks of deeper red can occasionally be seen traveling backward within the queue. These are denser clusters of vehicles temporary slowed down by lane changes. The vehicles in the cluster change as they emerge from the front and join it at the back, but the cluster travels as a wave packet backward through the stream. Vehicles experience these packets as the “slow-and-go” action. 


The simulation describes the evolution of traffic density on a three-lane freeway with a lane-drop at x2 when upstream demand increases gradually. Density is color-coded (red = dense or "queued"; green = light or "unqueued").  The simulation tracks all lane-changing vehicles, but only those that create a significant disruption are displayed (as blue rectangles).  The white portions appearing in front of each rectangle are portions of road without vehicles, caused by the lane changes. The figure also displays in real time (from left to right along the bottom): the oblique curves of cumulative count at the four detector stations; the cumulative number of lane changes; and two 30-second flow-density scatter-plots at locations x1 and x2.

The paper describing this model:

J A Laval and C F Daganzo. Lane-changing in traffic streams. Transportation Research Part B, 40 (3): 251-264, 2006. Preprint


Bertini, R.L. and Leal, M. ,"Empirical Study of Traffic Features at a Freeway Lane Drop.", Journal of Transportation Engineering, American Society of Civil Engineers, Vol. 131, No. 6, pp. 397

Cassidy M and J Rudjanakanoknad.  Increasing capacity of an isolated merge by metering its on-ramp. Forthcoming in Trans. Res. B; presented at 84th TRB Annual Meeting, 2004.