Shockwave traffic jams recreated for first time

Even moving slower will not prevent stop and go traffic if the road has reached its capacity, due to the various different accelerations and decelerations of cars. My overarching point is something like this video: [this video] There simply is not a way to avoid the consequences of being near or above a road’s capacity. Of course, I recommend everyone to play it safe and stay far enough back to avoid any liability of being too close to the car in front. But the reality is we make lots of calculations and choices in driving and at various times, we choose farther distances and other times nearer distances (even though we know it is riskier) and these collective decisions will propagate down through the whole road.

as far as i can read, your argument is that traffic jams are impossible, because congestion acts as a dynamic cost function to keep the road at its highest utility, when the throughput is highest. unless you disagree with the that definition of the utility of the road? how do you explain phenomena like shockwave traffic jams, where otherwise high utility roads get sections of nearly stopped traffic. eg. [this video] in a closed system (30s of video) can you spend some time showing your work, and both propose and prove what the cost function of congestion is? then, it should be clear whether the government set cost is higher or lower, and under what conditions. id especially want to see the limiting behaviour - standstill traffic. my gur sense is that the cost of congestion should be going towards infinity, but im interested in how the constant value from the government is still higher.

I'm going to double-down on this point because it does matter. In the real world some people are tailgating, but that does not cause traffic jams if and only if the road is running below peak capacity, where negative feedback self-corrects those traffic density deviations and gradually smooths everything back out. (Unless the tailgater causes a crash, of course). But if the average following distance is such that the road is exactly at the peak of throughput, or any smaller, then any momentary dip into tighter following distances pushes the road it into a positive feedback operating mode, which triggers a traffic jam. If you haven't seen it, here is a classic experiment demonstrating the effect: [this video] (But obviously the solution to traffic isn't 5 more lanes, it's viable alternatives to driving!)