H019
Twice the capacity, half the wait?
At a busy checkout, a second clerk doesn't cut the wait in half. It cuts it to almost nothing. On a busy freeway, extra lanes can leave the drive slower than before.
Capacity doesn't work in a straight line. A clerk who is busy 90% of the time has almost no slack, so every small rush of customers piles up into a long line. A second clerk absorbs those rushes, and the average wait drops from 18 minutes to about 30 seconds. A freeway is different because the number of drivers isn't fixed. When driving gets easier, people make trips they used to skip, businesses send more trucks, and new residents move in, until the road fills up again. Across U.S. cities, 10% more highway lanes brings about 10% more driving.
Before predicting what extra capacity will do, ask two questions: how close to full is it now, and will more people come once it's easier?
Try it somewhere else
A city doubles the size of a free parking lot downtown.
Why might the lot be full by 9 a.m. again a year later?
Why does a busy line grow so fast?
In a standard queueing model with customers arriving at random, the wait doesn't grow steadily as a clerk gets busier. It explodes near the limit. One clerk serving customers who each take 2 minutes on average:
| One clerk busy | Wait with 1 clerk | Wait with 2 clerks | How much shorter |
|---|
Two clerks share one line here. With two separate lines, waits are a little longer, because one line can jam while the other clerk stands idle, but the drop is still far more than half.
Where does the new traffic come from?
Economists Gilles Duranton and Matthew Turner compared U.S. cities from 1983 to 2003 and found that driving rose almost exactly in step with highway lanes. They called it “the fundamental law of road congestion.” The extra driving came from businesses and trucks, from residents taking more and longer trips, and from people moving to the city. Very little came from drivers switching over from other roads.
The Katy Freeway's slowdown also reflects Houston's fast growth in those years, so not all of it came from the new lanes. But the road filled up within a few years, as the fundamental law predicts.
So are extra lanes useless?
Not exactly. A wider freeway carries more people and goods, which has real value. What it usually doesn't do, for long, is make rush hour faster. Duranton and Turner found that adding buses didn't reduce traffic either. What has reduced congestion in practice is pricing: tolls that rise at the busiest times, as in London, Stockholm, and New York City, shrink the number of drivers instead of adding room for more.
Related exhibits
Sources: Checkout waits computed with the standard M/M/1 and M/M/2 queueing models (random arrivals and service times, one shared line), with an average service time of 2 minutes. Gilles Duranton and Matthew A. Turner, “The Fundamental Law of Road Congestion: Evidence from US Cities,” American Economic Review (2011), finding that vehicle-kilometers traveled rise roughly one-for-one with interstate lane-kilometers, and that bus service has no measurable effect on driving. Katy Freeway: $2.8 billion widening; peak travel times from Houston TranStar, 2011–2014, as reported by City Observatory (“Reducing congestion: Katy didn't”).