Queuing conundrums

tauringhuang.

Sep 11th 2008
From The Economist print edition

Strange as it might seem, closing roads can cut delays


DRIVERS are becoming better informed, thanks to more accurate and timely advice on traffic conditions. Some services now use sophisticated computer-modelling which is fed with real-time data from road sensors, satellite-navigation systems and the analysis of how quickly anonymous mobile phones pass from one phone mast to another. Providing motorists with such information is supposed to help them pick faster routes. But the latest research shows that in some cases it may slow everybody down.

Hyejin Youn and Hawoong Jeong, of the Korea Advanced Institute of Science and Technology, and Michael Gastner, of the Santa Fe Institute, analysed the effects of drivers taking different routes on journeys in Boston, New York and London. Their study, to be published in a forthcoming edition of Physical Review Letters, found that when individual drivers each try to choose the quickest route it can cause delays for others and even increase hold-ups in the entire road network.

The physicists give a simplified example of how this can happen: trying to reach a destination either by using a short but narrow bridge or a longer but wide motorway. In their hypothetical case, the combined travel time of all the drivers is minimised if half use the bridge and half the motorway. But that is not what happens. Some drivers will switch to the bridge to shorten their commute, but as the traffic builds up there the motorway starts to look like a better bet, so some switch back. Eventually the traffic flow on the two routes settles into what game theory calls a Nash equilibrium, named after John Nash, the mathematician who described it. This is the point where no individual driver could arrive any faster by switching routes.

The researchers looked at how this equilibrium could arise if travelling across Boston from Harvard Square to Boston Common. They analysed 246 different links in the road network that could be used for the journey and calculated traffic flows at different volumes to produce what they call a “price of anarchy” (POA). This is the ratio of the total cost of the Nash equilibrium to the total cost of an optimal traffic flow directed by an omniscient traffic controller. In Boston they found that at high traffic levels drivers face a POA which results in journey times 30% longer than if motorists were co-ordinated into an optimal traffic flow. Much the same thing was found in London (a POA of up to 24% for journeys between Borough and Farringdon Underground stations) and New York (a POA of up to 28% from Washington Market Park to Queens Midtown Tunnel).

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Modifying the road network could reduce delays. And contrary to popular belief, a simple way to do that might be to close certain roads. This is known as Braess’s paradox, after another mathematician, Dietrich Braess, who found that adding extra capacity to a network can sometimes reduce its overall efficiency.

In Boston the group looked to see if the paradox could be created by closing any of the 246 links. In 240 cases their analysis showed that a closure increased traffic problems. But closing any one of the remaining six streets reduced the POA of the new Nash equilibrium. Much the same thing was found in London and New York. More work needs to be done to understand these effects, say the researchers. But even so, planners should note that there is now evidence that even a well intentioned new road may make traffic jams worse.