Über ein Paradoxon aus der Verkehrsplanung.¶
Braess, D. (1968). Über ein Paradoxon aus der Verkehrsplanung. Unternehmensforschung, 12(1), 258-268.
Cited by¶
9 citations across 9 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Braess's Paradox
- Road traffic — the original 1968 setting: opening a shortcut can lengthen every commute under selfish routing; documented road closures in Seoul, Stuttgart, and New York improved flow.
This sourceOriginal demonstration that adding a road to a congested network with selfish routing can increase every driver's travel time; the canonical four-node example. (English: Braess, Nagurney, Wakolbinger, "On a Paradox of Traffic Planning," Transportation Science 39 (2005): 446–450.)
Supported in partVerified against the publisher's abstract
Braess's own abstract establishes the paradox in principle — extending a network may redistribute traffic and lengthen individual running times — but not that every commute lengthens, nor the Seoul/Stuttgart/New York closures.
“Furthermore it is indicated by an example that an extension of the road network may cause a redistribution of the traffic which results in longer individual running times.”
- Road traffic — the original 1968 setting: opening a shortcut can lengthen every commute under selfish routing; documented road closures in Seoul, Stuttgart, and New York improved flow.
- Nash Equilibrium
- This is more than theory — it predicts that adding a new road can raise everyone's travel time (the Braess paradox), because the new link shifts the best-response fixed point to a worse equilibrium, a counterintuitive result derived directly from the structure.
Supported in partVerified against the publisher's abstract
Braess's own abstract states the paradox outright — extending the road network may lengthen individual running times — but mentions neither a 'price of anarchy' nor a best-response fixed point shifting to a worse equilibrium.
“Furthermore it is indicated by an example that an extension of the road network may cause a redistribution of the traffic which results in longer individual running times.”
- This is more than theory — it predicts that adding a new road can raise everyone's travel time (the Braess paradox), because the new link shifts the best-response fixed point to a worse equilibrium, a counterintuitive result derived directly from the structure.
- Price of Anarchy
- Price of anarchy is the evaluative measure of how far a given mechanism's equilibrium falls from the welfare optimum — what mechanism design then tries to reduce. Not Tragedy of the Commons. The commons tragedy is a substrate-specific instance (over-extraction of a shared resource); price of anarchy is the general worst-case measure of which it is one case, quantifying the equilibrium-to-optimum gap. Not Braess's Paradox. Braess's paradox is the qualitative illustration that enriching a network can raise equilibrium cost; price of anarchy is its quantitative generalisation, bounding the loss over a whole game class.
Supported in partVerified against the publisher's abstract
Braess (1968) shows by example that adding a road link can raise travel times, supporting the claim's description of the paradox but not the price-of-anarchy generalisation.
“Furthermore it is indicated by an example that an extension of the road network may cause a redistribution of the traffic which results in longer individual running times.”
- Price of anarchy is the evaluative measure of how far a given mechanism's equilibrium falls from the welfare optimum — what mechanism design then tries to reduce. Not Tragedy of the Commons. The commons tragedy is a substrate-specific instance (over-extraction of a shared resource); price of anarchy is the general worst-case measure of which it is one case, quantifying the equilibrium-to-optimum gap. Not Braess's Paradox. Braess's paradox is the qualitative illustration that enriching a network can raise equilibrium cost; price of anarchy is its quantitative generalisation, bounding the loss over a whole game class.
Domain-specific¶
- Downs–Thomson Paradox
- The paradox belongs in a family of counterintuitive network results alongside the Braess paradox (adding a road link within a single-mode network can worsen equilibrium travel times for all users through selfish routing
Supported in partVerified against the publisher's abstract
“In einigen Fällen kann sich durch Erweiterung des Netzes der Verkehrsfluß sogar so umlagern, daß größere Fahrzeiten erforderlich werden.”
- The paradox belongs in a family of counterintuitive network results alongside the Braess paradox (adding a road link within a single-mode network can worsen equilibrium travel times for all users through selfish routing
Mechanisms¶
- Bypass Routing
- Its central failure mode is moving the jam instead of clearing it: pour a hub's worth of load onto an alternate that lacks the headroom and you have manufactured a second, larger outage — a congestion cascade that adding routes can actually worsen rather than relieve.
This sourceShows that adding a route to a user-optimized network can increase equilibrium travel time for every traveler.
- Its central failure mode is moving the jam instead of clearing it: pour a hub's worth of load onto an alternate that lacks the headroom and you have manufactured a second, larger outage — a congestion cascade that adding routes can actually worsen rather than relieve.
- Constraint and Boundary Reshaping
- Adding capacity or a new path can even make the system's equilibrium worse rather than better — the counterintuitive result named by Braess's paradox, where a new road can lengthen every trip.
This sourceDemonstrates the Braess paradox: adding a road can worsen the user equilibrium and lengthen every traveler's trip.
- Adding capacity or a new path can even make the system's equilibrium worse rather than better — the counterintuitive result named by Braess's paradox, where a new road can lengthen every trip.
- Edge Control Node
- Its failure mode is the local optimum that harms the network — every node greedily optimizing its own loop can degrade the whole, the way locally sensible routing choices can worsen total flow in Braess's paradox.
This sourceDemonstrates Braess's paradox, in which individually sensible routing choices can produce a worse aggregate network outcome.
- Its failure mode is the local optimum that harms the network — every node greedily optimizing its own loop can degrade the whole, the way locally sensible routing choices can worsen total flow in Braess's paradox.
- Logistics Routing Plan
- And naively optimizing a routed network can backfire outright — adding a shortcut or a route can, counter-intuitively, worsen total flow.
This sourceShows that adding a link to a user-optimized traffic network can increase equilibrium travel time for all users.
- And naively optimizing a routed network can backfire outright — adding a shortcut or a route can, counter-intuitively, worsen total flow.
- Micro-to-Macro Model Translation
- That is an emergent effect with no counterpart at the level of one driver.
This sourceShows that adding a link to a traffic network can worsen system-wide travel time even though individual drivers select locally advantageous routes.
- That is an emergent effect with no counterpart at the level of one driver.
Verification¶
Does it exist? Confirmed. This work's DOI resolves to a registered record, which fixes its identity. That is all it fixes.
Does it back the claim? Read against the text for 4 of 9 citations: 4 supported in part. Each verdict is shown under its citation below, with what in the work backs the sentence.
Support is checked per citation rather than per work — the same source can be cited soundly in one article and wrongly in another. Per-citation recording began recently, so a citation with no recorded check is a gap in the record rather than evidence it went unchecked.
See how references were verified.
Registry ID ref:7c7735eadfcd · see in the full table