Sarah Sheard's Thoughts and Theories

Saturday, November 11, 2006

Sarah's Theory of Steady State Traffic Jams

When you come to a clog in traffic, look behind you at how fast cars are arriving. You will get through the clog at approximately the same rate. So if you are behind 100 cars trying to get through a traffic light, and 12 cars are arriving every half-minute, you should be through the light in about 4 minutes.
(24 cars coming in behind you per minute means 24 cars will clear out in front of you each minute, so 100 cars will take about 4 minutes.)

This actually works fairly well in most situations, as long as the clog hasn't just happened. This is because most traffic patterns change slowly through a day, and for our purposes can be approximated by steady-state. If a clog is steady state, then just as many cars are coming into it as are going out of it. So if you want to figure out how long it's going to take you to get out of it, count the cars in front of you and the *rate* of cars behind you arriving.

Of course, this does not apply at all if there is an accident. Traffic can back up very quickly behind a new accident; thus, this cannot be approximated by a steady-state model.

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