Roads are at maximum efficiency always
On a theoretical road, the number of cars traveling is proportional to the speed of each car, so that the total number of motorists is constant regardless of speeds.
Assuming all cars are traveling at a speed that gives 3 seconds of time between cars, any change to speed limit cannot affect the traveler throughput, and each car added lowers the speed of all other cars, including those at the front.
Here’s a hypothetical example: a 9000m stretch of road has 0-dimensional cars[1] traveling at 30 m/s. Each car would be 90 meters apart, or 100 cars total on the road, taking 300 seconds for all cars to pass, or 1 car every 3 seconds.
Now, imagine that each car is going 15 m/s. Each car would be 45 m apart, with 200 cars. It would take 600 seconds for all cars to leave, with a car leaving every 3 seconds. (This works for any other numbers)
Any change to the speed causes the same change to the number of cars, and vice versa. The only variables a traffic engineer can change are the speed limits, and the time between cars.
This exercise implies that choices about efficiency are often tradeoffs from the total number of actions to the speed needed to perform each action. This could explain why businesses often give clearly unoptimal amounts of service, even though you will give your phone company more money if the service agent allows you to add money to your account.
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Obviously, this is a thought experiment, so we can ignore the fact that cars have length independent from their speed.
I don’t think this assumption holds. I don’t know what shape the actual speed-distance relationship is, but it’s not a straight line at a given number of seconds.
I also think the throughput measure (cars entering/exiting per hour) is rarely the most important thing for drivers or even planners. Average trip time outweighs it heavily.
Oh definitely—I don’t think this is practical advice for traffic designers
I’m a traffic engineer and I’m just cringing at this metaphor. Like, it’s probably a great metaphor, but the maximum throughput for cars is generally accepted as 1200 vehicles / lane / hour, and you have to keep these vehicles at a specific speed range, otherwise the traffic flow breaks down.
More info is this kind of thing: https://en.wikipedia.org/wiki/Fundamental_diagram_of_traffic_flow