The queue will clear
With perfectly coordinated acceleration and merging, cars use nearly all available road capacity. The queue still needs time to pass the bottleneck.
time = queue ÷ (outflow − arrivals)80 ÷ (30.0 − 15.0 cars/min) ≈ 5.3 min, plus incident recovery.
The same queue, demand, trucks, incident, and road—only driver behavior changes.
This is an explanatory traffic-flow model, not a prediction for a particular road. Every control below changes either demand, effective capacity, or the way a braking wave propagates.
Perfect drivers uses near-instant reactions and cooperative merging. Typical humans adds slower reactions and random braking. Rush hour pushes arrivals close to capacity. Phantom wave removes the physical incident so you can isolate stop-and-go behavior.
Initial queue is the stored number of delayed vehicles. New arrivals is continuing demand per hour. Arrivals stop after models a rush ending, a closed on-ramp, or ramp metering; “Continuous” leaves demand on indefinitely. This reveals whether better driving or simply fewer incoming cars clears the queue.
Driving perfection represents smooth spacing and acceleration. Reaction time controls how quickly simulated cars match the speed ahead. Cooperative merging preserves capacity; random braking introduces small human disturbances.
Bottleneck capacity is maximum hourly throughput after the obstruction clears. Incident remaining temporarily reduces it by 52%. Heavy vehicles reduce effective flow because trucks occupy more road and accelerate slowly—even when driven perfectly.
Run/Pause controls simulated time, Reset rebuilds the queue, and 1×/2×/4× changes playback without changing the result. Inject brake wave forces a short capacity loss so you can compare how perfect and imperfect drivers absorb the same shock.
Vehicle color reports state: cyan/gray is flowing, orange is delayed, and red is stopped. The dashed vertical marker is the bottleneck. Vehicles use a simplified car-following rule to accelerate, maintain space, and respond to the car ahead.
The dashboard reports queue size, model clearance time, average speed, discharge flow, backward queue-wave speed, and cumulative delay prevented versus typical behavior. The ± range tests an 8% capacity uncertainty rather than implying false precision.
The chart’s solid line is observed queue size; its dashed continuation is the current forecast. The comparison panel and animated clearance race hold demand, truck mix, incident, and road capacity constant while changing only driver behavior. A stalled racer marked “∞” means that version cannot clear under continuing demand.
Each vehicle occupies space and needs a safe time gap. Coordination raises the discharge rate, but cannot teleport a queue through a lane closure.
When braking—not a physical obstruction—causes the jam, perfect drivers prevent new shockwaves and damp the existing wave much faster.
If arrivals equal or exceed the effective outflow, the queue is mathematically unable to shrink. Better driving only slows its growth.