computer week · 28 September 2026

Lag and Margin

mean speed0km/h

spread0km/h, s.d. of speeds

stopped now0of 22 cars

contacts0gaps that reached zero

the ring's history waves grow

time ↓ newest at the bottom

0 mposition around the ring230 m

Lag1.00 s

Margin1.20 s

Cars22

tap a car to

lag and margin of the human drivers · drag the dot line: margin = 2.08 × lag; below it, linear theory says waves grow

stopped → 7 m/s calm driver ACC stopping zone within the gap stopping zone past the car ahead

What this is

Each human driver responds to the speed its gap allows and to how fast it is closing on the car ahead, using what it perceived one lag ago. The margin is the time headway it wants: at a margin of 1.2 s, a gap of 2 m plus 1.2 s of travel.

Linear theory says a disturbance grows as it passes back through a line of these drivers unless the margin is at least 2.08 times the lag. With the best possible gains the factor is 2.06; a driver who ignores closing speed needs 3.06. A small slowdown then grows into a jam that travels backward against the road while every car moves forward. The jam belongs to no car.

A calm driver drives at its leader's speed smoothed over 20 seconds and lets its own gap absorb the waves. An ACC car uses the commercial adaptive cruise control gains that Milanés and Shladover measured in 2014. It has no lag at all, and it still needs a 2.66 s margin to keep a line smooth. It keeps 1.1 s.

The line ahead of each car is its stopping zone (Gibson and Crooks, 1938): the distance it covers during its lag plus braking at 6 m/s². Where the line runs past the car ahead, that margin is spent.

Measured in the simulation	Value
Default humans (lag 1.0 s, margin 1.2 s): first stop	12–32 s (10 seeds)
Speed of the jam against the road	−10.1 km/h
Speed spread after four calm drivers join	4.1 → 0.4 m/s
ACC at 1.1 s margin: first stop	43 s

Limits: one lane, no intersections, no law. These model humans do not anticipate, so with a one-second lag they touch bumpers in the waves; the contact count says how often. Real drivers watch further ahead.