One of the enduring mysteries is what causes traffic jams. Sometimes it’s obvious — sort of. I remember having to make a daily trip from New York to Bellevue Hospitals in New York down FDR Drive. At one spot the three southbound lanes suddenly widened into five lanes because of some construction and then, after about 100 yards, narrowed again to three lanes. If you didn’t know better you’d think the extra capacity of the roadway wouldn’t be a problem but in your mind’s eye you can see exactly what happened. All those cars that filled up the extra space had to reconverge to three lanes. The roodway aneurysm caused a terrible mess.
More often, though, the cause isn’t so clear. Every year we drive about 1000 miles to a vacation down Interstate 95 and every summer, reliably as clockwork, we hit a bad traffic mess just south of Washington, DC in northern Virginia, usually just after midday. It’s always the same. Traffic flows at about 30 miles an hour, then suddenly jams to a standstill, then a few miles an hour, then back to 30 for a short period, etc. It’s like those old slinky toys, coiled springs that go down flights of stairs (if you’ve never seen one you have no idea what I’m talking about and if you have, you know how hard it is to describe; but there’s a great one on Wikipedia here). Slinkys had clear and obvious waves of compression-decompression moving up and down them and that’s what the traffic situation in Virginia felt like. But there never seemed to be a clear cause for this problem. As quickly as it appears it just stops, after about 20 or 30 miles of driving hell. Now a team of mathematicians at the University of Exeter have analyzed it and come up with what they think is a model that explains it:.
The team developed a mathematical model to show the impact of unexpected events such as a lorry (tractor trailer) pulling out of its lane on a dual carriageway (divided highway with median between traffic going in opposite directions). Their model revealed that slowing down below a critical speed when reacting to such an event, a driver would force the car behind to slow down further and the next car back to reduce its speed further still. The result of this is that several miles back, cars would finally grind to a halt, with drivers oblivious to the reason for their delay.
The model predicts that this is a very typical scenario on a busy highway (above 15 vehicles per km). The jam moves backwards through the traffic creating a so-called ‘backward travelling wave’, which drivers may encounter many miles upstream, several minutes after it was triggered. (Science Daily)
Essentially the model says the problem can start when the reaction of a single driver is propagated down the line when traffic density and flow is sufficient, somewhat like what happens in a smoothly flowing liquid that becomes turbulent when it reaches a certain point (as measured by its Reynolds number). But because this models driver behaviors rather than an abstract continuum, it is more comprehensible:
This model takes into account the time-delay in drivers’ reactions, which lead to drivers braking more heavily than would have been necessary had they identified and reacted to a problem ahead a second earlier.
Dr Orosz continued: “When you tap your brake, the traffic may come to a full stand-still several miles behind you. It really matters how hard you brake – a slight braking from a driver who has identified a problem early will allow the traffic flow to remain smooth. Heavier braking, usually caused by a driver reacting late to a problem, can affect traffic flow for many miles.”
Fascinating work I will enjoy pondering the next time I am stuck in a traffic jam. Which will probably be tomorrow on the way to work.
Addendum: Coturnix (Blog Around the Clock) alerted us to an excellent post he wrote about a year ago on this topic with some good links therein and some interesting observations of his own. Recommended if this topic interests you (as it does me).