Braess's Paradox
Braess's paradox is a result in traffic-network theory: under some conditions, adding a road can worsen travel times once drivers independently choose routes that seem best for them. The added link changes route incentives and redistributes traffic, potentially producing a less efficient equilibrium. The effect depends on network structure and congestion; it is not a general argument against building roads.
The paradox
Roads are often added to increase capacity, but the effect on travel time is not always beneficial. In a congested network, each driver's travel time on a route may depend on how many other drivers use its links. A new connection can alter which routes appear most attractive. If many drivers independently change routes in response, the resulting traffic distribution can leave everyone with a longer trip than in the network without that link.
Why individual route choices matter
The classic analysis treats route choice as decentralized: each traveler seeks a route with low personal travel cost, while link travel times change with traffic. At equilibrium, no individual can improve their trip by switching routes alone. This user equilibrium need not minimize total or average travel time for the network. In Braess's 1968 model, adding a link can redirect flow and raise the equilibrium travel time; removing a link can therefore sometimes improve the outcome.
A simple network illustration
A standard example has two routes from a starting point to a destination, each made of one congestion-sensitive segment and one segment with a fixed travel time. A new, very fast connector joins the middle of the routes. Once the connector exists, drivers may all find the combined route attractive. Their shared choices increase congestion on its approach and exit links, and the equilibrium can have a higher travel time than the equilibrium before the connector was added. The result arises from the interaction of route incentives and congestion, not because the new road itself is physically slower.
Scope and applications
Braess's paradox is a conditional mathematical phenomenon, not a universal prediction about road projects. Whether it occurs depends on link travel-time functions, demand and network layout. Traffic researchers use network models to identify cases where a new link might worsen equilibrium performance or where traffic controls could help. The same basic idea has also been studied in other systems with decentralized users and shared network capacity, but each application requires its own model and evidence.
Key facts
- Named after
- German mathematician Dietrich Braess, who published the result in 1968.
- Core idea
- Adding a link can increase equilibrium travel time in some congested networks when users choose routes independently.
- Key condition
- Travel costs depend on traffic flow and the network settles into a user equilibrium.
- Important limitation
- The paradox is possible, not inevitable; it does not show that road construction generally worsens traffic.
Ask about this article
Answers use only “Braess's Paradox” and its references, with citations.
References
- 1.On a Paradox of Traffic Planning
Transportation Science (INFORMS), translated 2005 version of Dietrich Braess's 1968 paper · other · reliability: unverified · retrieved 7 November 2026
- 2.Braess' Paradox
University of Massachusetts Amherst, Virtual Center for Supernetworks · other · reliability: unverified · retrieved 7 November 2026
- 3.Traffic congestion: Braess’ Paradox
The Network Pages · other · reliability: unverified · retrieved 7 November 2026
- 4.Braess's Paradox
The Engines of Our Ingenuity, University of Houston · other · reliability: unverified · retrieved 7 November 2026
References are suggested by the research engine and may be incomplete. Unverified URLs are omitted rather than guessed.
Article history
- Version 17 November 2026 · EditorCreated by Zapia