## The Emergence of Traffic Jams

This is something I have long suspected.  A short unexpected braking from one care propagates into a small traffic jam.   Reminds me of waves propagating in a flowing fluid.  Does traffic have a Reynolds number?

1. #### DaveK:

If I recall correctly, the chief cause of the "accordian" effect in urban traffic is the frequent lane-changing of a few drivers who switch whenever the adjacent lane is moving faster than their own.

2. #### DaveK:

Oh, another tidbit, from experience with a car-club:

If you're doing a group-road-trip and want to keep all the cars pretty much together, you need to put the slowest drivers in the front and the fastest at the last. If you do it the other way around, the cars will either get strung out and separated, or will begin "accordianing" as the lead drivers periodically slow to allow a straggler to catch up.

3. #### John_Schilling:

My professor and I tried to work out a fluid-dynamics traffic model many years ago. There probably isn't a Reynolds Number, as the existence of lanes suppresses the turbulent transition that Re is good for. We did conclude that the speed of sound in traffic is roughly 20 mph.

4. #### LoneSnark:

But when a road is near capacity, a short unexpected braking cannot be avoided, because on-ramps are a thing. For someone to get on, the people behind them must slow down. That slow down will propagate backwards increasing in severity to a full stop until it hits a gap in the cars large enough to eat it up. But, if it has propagated far enough back to be a full stop, then the car-free gap required to clear it can be a quarter mile long or more.

5. #### Roger Powell:

I don't think a Reynolds number applies here - that's mostly for identifying equivalent fluid flow dynamics (very useful for models in wind tunnels and so forth.) What you should be looking at is queuing theory which is a branch of mathematics very applicable to computer operating system design. It helps a designer understand and provision for what appear to be random backups but actually are mathematically predictable if you know the general distribution of events. Queuing theory helps determine how much resource over-allocation is needed.

Here's a quick example: Let's say you have a barber shop open all the time with an indefatigable barber who takes exactly 15 minutes to cut someone's hair. Let's also say that customers appear randomly distributed in time (Poisson distribution) but on average once every 15 minutes. If a customer arrives and the barber is busy, he waits in line.

The question is: How long is the line on average? The answer is counter-intuitive: The line grows over time to infinity.

So what's my point? Traffic engineers (like computer operating system designers) need to over-allocate resources because of the "choppy" flow (in this case, random brake taps, lane changes, etc.) to avoid unexpected backups. The experiment in the video is a giant waste of time as the result is already well-known and predictable.

6. #### Pete Chiarizio:

I think you're looking for a kinematic wave mathematical description, not a fluid dynamics mathematical description.
I've seen computer models of this on TV somewhere - 1 dope doing 40 on the highway screws the whole road up.
I work with traffic engineers and congratulate them every morning on the fine job they've done creating tons of traffic virtually everywhere.

8. #### scp:

Related:
TRAFFIC "EXPERIMENTS"
AND A CURE FOR WAVES & JAMS
http://www.amasci.com/amateur/traffic/trafexp.html

9. #### TCNM:

The fluid analogy is correct but the fluid is compressible and governed by hyperbolic partial differential equations. Traffic chokes and and also forms shocks and rarefactions. See Leveque, Finite Volume Methods for Hyperbolic Problems. Cambridge, 2003.

10. #### chembot:

There was a popular science book a few years ago authored by Steven Strogatz called "Sync: How Order Emerges From Chaos In the Universe, Nature, and Daily Life" that cast traffic in terms of chaos theory. Pretty interesting read in general about how order spontaneously appears from chaotic systems.

11. #### irandom419:

To me it is a longitudinal wave. People will speed like hell to merge, but when leaving one of these "kinks" they are cautious as all hell.

12. #### kidmugsy:

A friend of mine analysed traffic jams in a course he taught on (I think) compressible flow: his model resulted in shocks. I don't think it was original; I have a memory that he told me that he'd come across it in the literature somewhere.

13. #### BobSykes:

There is an enormous literature about this in the traffic engineering journals. A long-deceased colleague of mine, Joseph Treiterer, produced a famous movie of the phenomenon. It was shot from a small aircraft that flew over I71 in Columbus.

14. #### Todd Ramsey:

This phenomenon can be eliminated/reduced by variable speed limits during periods of overcapacity, coupled with severe penalties for exceeding the speed limit.

15. #### marque2:

Studies have actually shown that the lane changers actually help improve the traffic flow.

16. #### DaveK:

The ones I refer to are the ones who change lanes with minimal warning and cause the cars behind them in the "faster" lane to suddenly brake to maintain safe spacing. If you can make the lane change without disrupting the traffic in the lane you're entering, you've done quite well.

17. #### jdgalt:

Most traffic jams are neither the fault of traffic engineers nor drivers, but are deliberate on the part of urban planners, who constantly purvey the myth that building roads "induces" demand. Let the market supply all the roads drivers want to pay for, and that myth will be disproven on the spot. But most of the public are sheep, so it will continue to get worse.