Can building more roads make traffic worse? Here’s the mathematics behind it

Tackling traffic congestion is one of the biggest challenges facing large cities around the world. When it comes to reducing congestion, one solution almost instinctively comes to mind: build more roads or widen existing ones.

But the science of transport economics has shown for decades that increasing road capacity does not necessarily translate into smoother traffic. In fact, under certain conditions, it can do the opposite.

Here’s how it works.

A simple road network

Let’s start with a very simple road network.

Suppose everyone in a town lives at the same origin (the start) and travels each morning to the same destination (the finish). There are only two possible routes between them: the first route goes from the start to point A, then from A to the finish; the other goes via point B instead.

The roads from the start to B and from A to the finish are nice and wide, and take a constant 45 minutes regardless of traffic. The roads from the start to A and B to the finish are narrower. They take five minutes without traffic, but every 100 cars on the road adds an extra minute to the trip.

During the morning peak, 4,000 drivers go from the start to the finish each day. The question is: how do the 4,000 commuters distribute themselves between the two routes?

Finding equilibrium

Transport scientists answer this using the concept of traffic equilibrium. A road network is in equilibrium when no commuter can reduce their travel time by changing routes.

If one route is quicker, some drivers would switch to it. That movement would continue until no driver could improve their journey by choosing differently.

In our simple network model, the equilibrium is straightforward to calculate. It occurs when 2,000 commuters use each route.

In this situation, each wide road (from the start to B and from A to the finish) takes 45 minutes, and each narrow road (from the start to A and from B to the finish) takes 25 minutes. So, each route takes 70 minutes in total to complete.

Adding a new road

Now suppose the city builds a new one-way road connecting A to B. It takes just ten minutes to traverse, no matter how many people use it.

Commuters now have three routes to choose from instead of two: they can travel from the start to A to the finish, from the start to B to the finish, or the new route from the start to A to B and then to the finish.

It seems difficult to imagine how this could make anyone worse off.

But remember how drivers choose their routes. They are not trying to minimise congestion across the network. They are trying to minimise their own travel time.

After the shortcut is built, if most drivers stick to the original routes but one driver uses the shortcut (travelling from the start to A to B and then the finish), that one driver can do the whole trip in 60 minutes (25 minutes from the start to A, ten from A to B, and 25 from B to the finish).

However, when many drivers use the shortcut the congestion levels change significantly. The network eventually settles into a different equilibrium.

Half of all commuters (2,000) now use the new route, while the remaining commuters split evenly between the two original routes. As a result, the two congestion-prone road segments each carry 3,000 commuters instead of the previous 2,000.

As a result, every route now takes 80 minutes to complete – ten minutes longer than before the new road was built.

Selfish versus socially optimum choices

The paradox could be avoided if commuters coordinated their decisions and agreed not to use the new connection. With 2,000 commuters on each original route, everyone would again complete the journey in 70 minutes.

This is called the system optimum or social optimum: the traffic pattern that minimises total travel time across the network.

But it would not be a stable condition. Any single commuter could leave the coordinated arrangement, use the shortcut and save themselves ten minutes.

Others would have an incentive to follow suit. As more commuters make that selfish choice, the network eventually returns to the 80-minute user equilibrium.

The problem: what is best for each traveller individually is not necessarily what is best for travellers collectively.

What does all this mean in practice?

This simple example might give the impression that the phenomenon is little more than a mathematical curiosity. But theoretical studies have shown this situation can arise in much larger and more realistic transport networks.

In fact, identifying road segments that can be removed to improve overall network performance is an area of research in its own right.

A growing body of practical research is also evaluating the effect of highway and freeway removal projects in cities around the world.

The paradox has also been tested experimentally, showing it can emerge through actual human decisions in laboratory settings.

Our example also made one notable assumption: that the number of people travelling by car remains unchanged after a new road is built.

In reality, expanding road capacity often encourages additional car travel. This is called “induced demand”. It can further reduce the long-term congestion benefits of new road capacity.

Roads in the real world

Direct real-world demonstrations of this paradox are inherently difficult. It is rarely possible to isolate the effect of a single road addition or removal while holding all other factors constant.

Nevertheless, several well-documented road closures and highway removals have produced outcomes broadly consistent with the theory. These include the removal of the Cheonggyecheon Freeway in Seoul, and the closure of 42nd Street in New York during the 1990 Earth Day event.

None of this means that building new roads is always counterproductive, or that removing roads is always good. The key point is more nuanced.

Road expansion should not be viewed as a guaranteed remedy for congestion. Without considering how travellers respond and how the wider transport network adapts, it risks becoming part of a repeating cycle: new road capacity is gradually absorbed by changing travel patterns, leading to renewed congestion and, ultimately, the need for yet further road expansion.