How can adding a shortcut make everyone’s journey slower?

A new road gives drivers more choices, but their choices also change congestion. Braess’s paradox describes networks in which opening an extra connection can worsen the travel time reached when each driver chooses a personally faster route.

Consider an invented model with 100 travelers. Two routes connect start to finish. The upper route has a congested segment costing its traveler count divided by 10 minutes, followed by a fixed 12-minute segment. The lower route reverses that order. With 50 travelers on each route, each trip takes 5 + 12 = 17 minutes.

Now add a zero-time link from the upper middle junction to the lower one. A traveler can use both congested segments and skip both fixed segments. In the resulting all-shortcut pattern, each congested segment carries 100 travelers, so every trip takes 10 + 10 = 20 minutes.

No single traveler benefits by returning to either old route: it would cost 10 + 12 = 22 minutes while the others remain. Individually sensible choices can therefore settle into a slower shared outcome. Coordinated routing could still preserve the old split; the extra road has not physically erased it.

This is a conditional mathematical example, not a claim that new roads always hurt. It reveals why network design must consider incentives and feedback as well as the number of available connections.