Han et al. (2602.22019) explain why the traffic leaving a traffic jam is always slower than the road's theoretical capacity, and the answer is hesitation.
Capacity drop is one of those phenomena that everyone who drives has experienced: the bottleneck clears, but traffic doesn't snap to full speed. The discharge flow runs at 5-15% below what the road should support. Various theories have been proposed — lane-changing disruptions, acceleration delays, driver psychology. Han et al. build an analytical model around the simplest version: some vehicles stochastically hesitate during acceleration, creating temporary voids (extra gaps) in front of them.
The key insight is the interaction between these voids. A hesitant vehicle downstream creates a deceleration wave that propagates upstream. An upstream hesitant vehicle creates its own void. When the downstream wave reaches the upstream void, the two interact — the wave partially absorbs the void or the void partially absorbs the wave. The net effect depends on geometry: their relative positions and timing.
This interaction mechanism explains a puzzle from prior empirical work: standing queues and moving jam waves show different amounts of capacity drop despite having similar discharge conditions. In a standing queue, downstream hesitant vehicles are ahead of upstream ones in the flow direction, so their waves and voids interact constructively (both reduce throughput). In a moving jam, the geometry is different — the jam wave itself introduces a phase relationship between hesitators that partially cancels the void interaction.
The model validates against real trajectory data. But the conceptual point generalizes: the performance loss from a queue isn't just the sum of individual delays. It's the interference pattern between perturbations, which depends on the spatial structure of the queue itself. The queue shapes the discharge that the discharge shapes the queue.