Zipper merge: perfect vs. human

Three roads of two lanes with the right lane merging into the left lane. New cars arrive at the same rate in the same way on all three. In the perfect zipper, drivers correctly adjust velocity and spacing to merge. In the two imperfect zippers they fail to adjust velocity or make room or look for a spot by accounting for their neighbors. In the second one they go all the way to the end, and in the third they start looking for a merge spot a few meters back.

Speed cars arrive at, and the speed limit through the merge.
Typical error in judging a gap, for drivers in both lanes (roads 2 and 3). Also slows reactions to a merger.
Share of drivers (roads 2 and 3) who, stuck in the left-lane queue, pull into the emptier right lane to get around it and then merge back in.
Cars per hour per lane. One lane carries ~2,800/h at 55 mph, but random bunching means even perfect drivers start slowing above ~1,100 per lane.

Reading the roads

Red tail lights mean braking; a large red glow means braking harder than 4.5 m/s². A blinking amber light means the driver is trying to merge.

How it works

  • Car following. Every driver follows the car ahead with the Improved Intelligent Driver Model (1 s headway, 1.5 m/s² acceleration, 2 m/s² comfortable braking, 9 m/s² emergency).
  • Road 1, perfect zipper. The merge order is simply the order cars joined the road, in either lane. From the moment they enter, every car eases back from the car before it in that order, so by the merge point each has exactly a normal following gap: one from each lane, at speed, with nobody braking to get in. Queues form only if more cars arrive than one lane can carry.
  • Looking for a gap. On roads 2 and 3, a right-lane driver keeps driving normally until their try point, then signals and starts looking. While looking, most just drift back a little (to at most 2 m/s slower than the left lane) to line up with a gap, and merge as soon as one looks big enough; a hesitant minority (more with more skill variation) slow down further, to as little as half speed. The left-lane car behind who notices the signal lets that one car in. If the lane runs out with no gap, they brake and stop at the end.
  • Gap judgement. A driver merges only if they think neither they nor the car behind will need to brake harder than 3 m/s². With skill variation, every driver sees gaps scaled by a personal bias (plus moment-to-moment noise for mergers), and left-lane drivers react 0.3 s or more late. Optimistic mergers cut in too tight and force the car behind to brake hard; pessimists turn down good gaps and run out of lane. Left-lane drivers misjudge too: some open too small a gap, some hang back too far.
  • Queue jumpers. On roads 2 and 3, the share of drivers you set will, when crawling in the left-lane queue at least 100 m before the merge point, pull out into the right lane if it is clearly faster and there's a safe gap, drive past part of the queue, and start looking for a way back in 20 m after pulling out.
  • Road 2 only starts looking 25 m before the merge point. Road 3 has the same drivers, but each starts looking at their own distance, spread around the median you set.
  • Fair comparison. All three roads get the same arrival times and the same drivers (gap-judgement bias, reaction time, cruising speed within ±10%). Press Reset for a new random stream.