Those who use the bike know this very well: in the city, speeding motorists overtaking other cars, only get one thing: they arrive first to the next red.
With a simple model, the author estimated the probability that one car that overtakes another, will then be reached again at a later red light. Then he estimated the probability that the same thing will happen when there are multiple successive traffic lights, as usual in the cities.
The result is that as fast as an aggressive driver goes, the presence of multiple traffic lights makes it virtually certain that a slower driver will catch up
So, if someone aggressively overcomes you, when you reach him at the next traffic light, you can tell him that it is mathematically proven that he/she is an idiot.
In addition, this study has implications for the 30 km/h city, demonstrating how in urban areas the traffic lights determine the travel times, not the maximum speed reachable between one traffic light and the next.
The original scientific article is here: https://royalsocietypublishing.org/rsos/article/13/4/260310/481212/The-Voorhees-law-of-traffic-a-stochastic-model
crossposted from: https://poliversity.it/users/rivoluzioneurbanamobilita/statuses/116419204210303856
My mental model is slightly different. I think of average speed of the car between source and destination. Every segment of the road will have an average speed at a given time, which may vary depending on the time of the day. This average speed is dictated by numerous factors, including traffic lights, number of slow vehicles on the road, speed limits, etc. You cannot really go significantly higher than this average speed, even if you try as aggressively as possible.
There are exception, especially in Asian roads. If you are a large vehicle, who doesn’t care about the law and limits, and they do very aggressive driving, then they go at a larger average speed. I have some completely asshole private bus services in my country.
My very spread out city has two roads between its southern suburbs and the city, each is about 30km long
Both only have speed cameras to control speed
So most people drive at what their car tells them is the speed limit, which almost always is 5km/h slow, then a few follow of public safety advice and drive 5km/h under the limit, so actually at -10 and very few have accurate speedometers or GPS that tells them their actual speed and try to travel at the speed limit, and a small number deliberately speeding
Then when we reach the speed cameras the cars going slow all slow more, the speeding cars slow down to well under the limit, and the very few confident drivers try to continue at the limit
Traffic is really smooth and will behaved before the speed cameras, and a hundred metres after them
I find people who say this don’t properly account for their time waiting at lights. Sure, you may be going faster when you aren’t stopped, but you will catch those reds more often and will be stopped longer, reducing those average speeds. Which is the entire point of the article.