On Traffic

I spend an hour to an hour and a half on Auckland freeways every working day of my life. This gives me plenty of time to listen to music and think about blog posts (if I could write them in traffic, I would be a happy man!) It also gives me plenty of time to observe traffic itself and especially the phenomenon of phantom traffic jams. You know what I’m talking about, right?  Except you guys in Invercargill who think a traffic jam is half a dozen cars, waiting at a traffic light. I’m talking about when the traffic slows to a crawl or stops altogether and then, suddenly, after a few hundred meters of snail pace, opens up back to normal flow for no reason at all. No accident, no Fulton-Hogan-inspired obstruction, not even a police car. Just nothing at all.

Wired Magazine ran an article some time ago about MIT doing some mathematical modeling around the dynamics of traffic. Even someone stepping over-enthusiastically on their brakes due to a moment’s inattention can cause a snowball-like effect and create a traffic jam (or “Jamiton” as the MIT guys called it – from a type of standing wave called a soliton). Apparently the mathematics of phantom traffic jams resembles the event horizon of a black hole.

Tell me about it.

They present this really cute little graphic demonstrating the wave effect in traffic – anyone familiar with rush hour will recognise it instantly:

Apparently all of this occurs because traffic exceeds the capacity of the road – a figure known as critical density. Which is why traffic engineers think that traffic lights on on-ramps work. Sure they back up the traffic on the side roads, but they go some way to preventing the motorway from exceeding critical density and jamming solid.

Counterintuitively, the way to counteract jamitons is to slow the traffic down. There is an elegant experiment described in Tom Vanderbilt’s book Traffic, in which rice is poured into a funnel. When the rice is dumped in all at once, it takes 40 seconds to clear the funnel. If it is poured into the funnel in a thin stream it takes a mere 27 seconds. Slow traffic entering the main arterial road and you prevent the jam.

Even more counterintuitively, blocking some roads altogether can help move traffic. Apparently, the journey time for all routes eventually averages out. If you allow many alternative routes, the average time is lengthened for everyone. This actually does make sense. The transit time for minor routes when blocked is much longer than the transit time for the major route. Therefore the point of Nash equilibrium, where there is no advantage to taking an alternative route, is longer than it would be if everyone took the main arterial routes.

You see the same thing happening on the freeway. Cars hop from lane to lane, hoping to gain an advantage but only succeeding in slowing the flow for everyone. The faster lane always slows when traffic move into it (being cut off by someone is an excellent cause of a jamiton!). The slower lane briefly speeds up, only to be slowed by the Weaver Birds (Weaving from lane to lane). Eventually the lanes settle to a Nash equilibrium considerably slower than if everyone stayed in their lane unless entering or leaving the freeway.

And don’t talk to me about the sight of cops ticketing people in the middle of rush hour traffic (guaranteed jamiton), I get somewhat homicidal on the topic.

Hat Tip: Freakonomics

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