Stopping Traffic

Since coming back to Florida and commuting every day, we've noticed that the traffic lights stay on a particular direction for a long time before switching. This is especially annoying as a pedestrian (who dislikes jaywalking), since it means the walk from the parking lot to my office can vary a lot depending on what lights I hit. I was curious whether I could design a simulation to test the effect of the light duration on the time cars spend waiting.

The setup is a 4-way intersection with lights that swap red/green with separate green durations for North/South and East/West. Each road has a rate cars arrive, and each car randomly chooses to go left, right, or straight. As cars pass through the intersection, we can keep track of how long they had to wait since arriving. Below is an example simulation – The arrows are the lead cars on each road, pointing in their planned direction and colored to indicate how long they've been waiting.

We've got a lot of variables going on here, so it took me a while to figure out how to assess the results. It would take too long to try every combination, so I just sampled from a reasonable-sounding range. I considered using a corner plot to see the effects of the inputs, but the sampling was too sparse to see a trend. One way to reduce the number of parameters is to consider where each car is coming from, and use the traffic rate and light duration from that side. Then I thought about the units: the traffic rate measures cars/time, and the light duration is a time, so multiplying them gives an average number of cars during a green light. Plotting this with the waiting time shows a clear trend:

I separated out the different turning directions, expecting that left turns would need to wait longer, but that doesn't seem to be the case. This shows that to minimize the waiting time, we need to keep the rate*duration small, i.e. for busy roads the lights should change rapidly, which is not what I expected.

This also implies that the Florida lights are expecting a low rate of traffic – Not our experience the past few weeks coming home during rush hour and hitting gridlock! Of course, this model may be inaccurate, and I should stick to gravitational waves, rather than civil engineering.