Leaving space does not increase the average speed, because the average speed is dictated by the MAXIMUM speed in addition to the number of cars on the road.
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First we must assume we live in the 3rd dimension of a physical realm, wherein objects like cars cannot pass through other objects. Cars can not drive through other cars, thus, if one car stops or slows down, all cars behind it stop or slow down.
Second, 5000 cars cannot travel 65mph over one mile of road, because it is physically impossible to fit 5000 cars inside a one lane 1-mile stretch of road. This is the bottleneck that causes the initial traffic jam.
In order to get all 5000 cars to travel the distance of a mile in the same TIME as 1 car, your only option is to increase their speed. But our speed is limited (by the speed limit of the road), so the only thing we can do is squish them together and hope for as fast a speed as possible given the dimensions.
If all the cars were linked and communicated in unison, they could react immediately and maintain a high degree of coordination in moving around each other and traveling as fast as the number of cars and speed limit will allow over a given area. Unfortunately, humans suck ass at driving, and their communication and latency make the movements of cars much much slower than is theoretically possible.
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So what does "leaving space" actually do within our constraints of number of cars and max mph? It smooths out the errors humans make in driving. Specifically, it adds a time buffer for communication and decision-making; more time is given to driving decisions in order to prevent unnecessary stops, which would slow or stop the cars behind it.
What "leaving space" does NOT do is change the laws of our physical world. The given number of cars still have a maximum possible speed in a given distance, due to the traffic laws and physics.
Is it possible that the buffering from leaving space in the road will cause traffic to actually move faster than the starting-and-stopping of human error? Yes.
But it also uses up additional space, which is equivalent to more cars on the road, which as we know from above means a lower speed to travel the same distance.
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You can not get away from it - until you reduce the number of cars or increase the max speed, your traffic jams will remain.
As for my personal opinion, I believe the one thing that could reduce traffic slowness is to speed up merges. If you want to help a traffic jam, merge at a speed faster than the cars around you and accelerate away from the merge area. It won't permit more cars on the road, but if a car is going 45mph and you move in front of it going 35mph, physics only allows for two results: the car behind you will hit you, or the car and all the cars behind it will have to slow down to 35mph.
The other thing that could be done is sensors in the road could detect the level of traffic (number of cars) and provide on a digital display the maximum speed humans could manage for that many cars on the road. If all cars then traveled at that speed, we would slowly but at a continuous pace travel down the highway without any stops. Until the first asshole that merges slower than that speed, which would make everyone slow down to his speed, defeating the whole thing....
