On the Existence of Equilibria in Asymmetrical Multiclass-User Transportation Networks

Dietrich Braess

40 citations0/0 files storedTransportation Science

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Transportation Planning and Optimization Traffic control and management Optimization and Variational Analysis

Abstract

When studying multiclass-user transportation networks Dafermos made a strong assumption on symmetry in order to prove existence of a user-optimizing flow pattern. In this paper existence is proved without the symmetry-hypothesis and it is shown that the methods of convex programming are not applicable.

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References

1968Über ein Paradoxon aus der Verkehrsplanung 1972The Traffic Assignment Problem for Multiclass-User Transportation Networks 1970Braess's paradox of traffic flow 1972Flows in Transportation Networks 1971An Extended Traffic Assignment Model with Applications to Two-Way Traffic 1976Traffic Equilibrium Methods

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2005The Downs-Thomson Paradox: Existence, Uniqueness and Stability of User Equilibria 2015A piecewise-constant congestion taxing policy for repeated routing games 2005Preface to “On a Paradox of Traffic Planning”2019Pricing Traffic Networks with Mixed Vehicle Autonomy 1998Perturbation stability of the asymmetric stochastic equilibrium assignment model 1986Road traffic assignment — a review 1983Modéles De Distribution Spatiale Tenant Compte Des ItinéRaires 1986Road traffic assignment—a review

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