[Retric]

Your model suggests we should get thousands of car pileups if anyone does heavy breaking in bumper to bumper traffic. Clearly that does not happen.

The reason is the buffer between you and the car in front of you is eaten by the difference in your speeds. Going from 80MPH to 70 MPH takes ~0.7 seconds, where starting to break takes ~0.2 seconds. Even if there is just 5 feet between cars the signal propagates plenty fast.

[zo1]

What do you mean by difference in speeds? The assumption I made, simplifying the thought experiment, was that the cars had a fixed-length between them, and they were all going at the same speed.