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I noticed that on a road, if the number of cars reaching a certain critical stage, all the cars would slow down immediately.

Is there any theory/model that connects the number of cars $N$ with the average car speed $V$, and maybe with road width $R$ ( and other variables)?

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You might be looking for traffic flow: en.wikipedia.org/wiki/Traffic_flow –  Qiaochu Yuan Mar 15 '11 at 15:03
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You might be interested in the answer to this related question: math.stackexchange.com/questions/11231 –  Mike Spivey Mar 15 '11 at 16:06
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