Traffic Signal Math

The other day, for some reason (maybe because I was sitting at a traffic signal, or rather quite a distance back from a traffic signal), I remembered that I had written a paper in high school about the way traffic behaves at a traffic signal. I’m sure it was written as part of an English class, but that is about the extent of what I can recall about it. This got me thinking, “If I were to write a paper today about traffic behavior at a traffic signals….?” So (you guessed it), I wrote one.


Sitting at traffic signal the other day, I was about 15 cars back from the signal. I was at the top of a hill looking down on the line in front of me, so had pretty good visibility of what was happening. As I’m sure we all have at one time or another, I noticed that the light would turn green, a few cars would go through, then the light would turn red again, all before the cars directly in front of me ever began moving. After seeing this happen a couple of times, I started thinking about why this happens.

Remembering from my youth (and some quick Googling) that a perfect reaction time off the line for drag racers is .500 seconds, and figuring in a bunch of other considerations, I thought I might be able to figure it out.

Obviously, if everyone in line at the light were to react to the light changing from red to green at the same time, all the cars in the line would start moving at the same time. Since I’ve never seen all the cars in a line start moving at the same time, I am going with the assumption that drivers at a traffic signal will, in general, react not to the changing of the traffic signal itself but to the reaction of the car immediately in front of them.

I did a (very unscientific) survey of response times at the neighborhood traffic light and found that response times vary from just over a second (for the guy sitting there watching the cross traffic light go from yellow to red) to about 4 seconds (for the cigarette smoking, coffee drinking, cell phone talking general menace). For ease of use, I’ll use an average of a 2.5 second reaction time.

Once you have the average reaction time, simple multiplication will tell you how long it will be before you start moving. So being 15 cars back, it would take about 37 seconds from the time the light changes to the time I start moving. If the light only stays on for 30 seconds, you won’t even begin moving until 7 seconds after the light changes back to red.

I’ll leave it to you figure out, based on this and a little bit more info you’ll have to gather for yourself, how many cars will actually get through the light.

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