By 2 sec following distance I am referring to their back bumper to your front bumper. So cars "overlapping" in your example is not possible
If you want 4 sec gap at higher speeds that's fine, the formula is speed-independent for throughput, not speed-independent for following distance. If you want 4 seconds at high speed then use 4 sec instead of 2 sec (i.e. 1 car/ 4 sec)
>There's also the issue of speed oscillations. With a high speed limit and vehicles following too closely, a little variation in speed in one vehicle can turn into a larger variation in the following vehicles, causing a backwards-travelling wave of braking (sometimes to an absolute halt) and speeding up again. Lowering the speed limit reduces this.
"Lowering the speed limit reduces oscillations." Exactly, that is my whole point, that (again, locally analyzed) you can ignore the waves, and instead look only at the following distance of the slowest car in the lane, to determine throughput of the road behind that car. Your idea of "lowering the speed limit" to eliminate waves is the same net effect on throughput as observing that the throughput cannot exceed that given by the longest-following car on the road.
A niggle - if you are referring to a 2 second gap between the back bumper and the following front bumper, then the formula is no longer speed independent, as you need to add the small overhead to account for the time taken for the length of the vehicle to pass as well. This will be small enough to be mostly negligible except at low speeds.
If you want 4 sec gap at higher speeds that's fine, the formula is speed-independent for throughput, not speed-independent for following distance. If you want 4 seconds at high speed then use 4 sec instead of 2 sec (i.e. 1 car/ 4 sec)
>There's also the issue of speed oscillations. With a high speed limit and vehicles following too closely, a little variation in speed in one vehicle can turn into a larger variation in the following vehicles, causing a backwards-travelling wave of braking (sometimes to an absolute halt) and speeding up again. Lowering the speed limit reduces this.
"Lowering the speed limit reduces oscillations." Exactly, that is my whole point, that (again, locally analyzed) you can ignore the waves, and instead look only at the following distance of the slowest car in the lane, to determine throughput of the road behind that car. Your idea of "lowering the speed limit" to eliminate waves is the same net effect on throughput as observing that the throughput cannot exceed that given by the longest-following car on the road.