# Chaotic traffic

Most of us have experienced flowing freely down the highway, then for no apparent reason find ourselves slowed to a creep. Sometimes, I recall, this arises from a chaotic effect. How can the automotive public actively avoid traffic jams of this nature, those caused by chaotic patterns in driving?

matt grime
Homework Helper
Please don't bandy about words like 'chaotic' that have a strict mathematical meaning (or set of meanings). 'No apparent reason' is not 'chaos'. Abusing terms like that doesn't paint you in a good light.

tony873004
Gold Member
What would be the correct term? I've noticed this effect too. And it would make sense to me that it is sensitive to initial conditions. One fewer car on the road, or one car displaced by a small distance might just cause the slowdowns to happen in different places, or at different speeds.

Before looking to chaos, I might guess that traffic lights on city streets have an effect. When the light turns green, a bunch of cars hop on the on-ramp and form a concentration of cars on the freeway. As these concentrations catch up to each other, it may cause slowdowns.

A friend of mine has a nice view of the freeway from his window. He made the observation that when traffic is light, that cars tend to drive in packs. We watched for a few minutes, and he was right. You'd see 7 or 8 cars, then nothing for a half mile, then 5 or 6 cars... We guessed traffic signals at the onramps caused the groupings.

I think this subject has been studied in England under a title like, Queueing Theory. A queue being a line you wait in. There was once, I remember, a paper or book called, "Why do Buses Come in Threes?"

I used to wonder about the lunch line. Lunch was between 12 and 1 and it took from 5 minutes to 1/2 hour to get the lunch, all depending upon when you and others showed up. (The line length was not constant, but changed everyday. Many evidently trying to come when the line was short.)

Here is something I found roaming the internet: Despite the apparently chaotic transport system, there is a sort of statistical order in the collective behavior of the vehicles. Physicists Petr Seba and Milan Krbalek of the Czech Academy of Sciences have found that Cuernavaca buses move about like randomly interacting subatomic particles. This activity can be described in terms of mathematical expressions called random matrices, which were originally used to describe the quantum energy levels of large atoms or heavy atomic nuclei. http://www.sciencenews.org/articles/20010324/mathtrek.asp

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chroot
Staff Emeritus
Gold Member
The bottom line is that "compression waves" ripple down the freeway, causing brief periods of stop-and-go traffic for no apparent reason.

All of the same phenomena you can observe with sound waves -- standing waves caused by obstructions, travelling longitudinal waves caused by compression, etc. -- can be observed in traffic flow.

An accident long since cleared from the roadway can still affect traffic patterns for pretty much an entire day. Many times these "mini jams" are ultimately caused by events that occured hours ago.

- Warren

I apologize that I should have used the term "nonlinear" rather than necessarily "chaotic." At least that is what I recall learning.