Optimizing Traffic System Performance with Environmental Constraints: Tolls and/or Additional Delays

Lin, Xin; Tampère, Chris; Proost, Stef

doi:10.1007/s11067-019-09471-8

Cited by 4 publications

(1 citation statement)

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“…( ) If, however, the Jacobian of C is not symmetric, the integral in (1) will depend on the integration path P. In what follows, we propose a way of interpreting the integral and then build an equilibrium model whose every solution satisfies the conditions in (5). It is possible to include additional restrictions to the problem, associated for example with restrictions on environmental emissions (Lin et al, 2020), but this is outside the scope and objective of this work.…”

Section: The Above Expression Is Clearly a Generalization Of The Obje...mentioning

confidence: 99%

Generalization of Beckmann’s Transformation for Traffic Assignment Models With Asymmetric Cost Functions

Maréchal

Grange

2022

Preprint

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An optimization model is developed to solve the deterministic traffic assignment problem under congested transport networks with cost functions that have an asymmetric Jacobian. The proposed formulation is a generalization of Beckmann’s transformation that can incorporate network links with multivariate vector cost functions to capture the asymmetric interactions between the flows and costs of the different links. The objective function is built around a line integral that generalizes the simple definite integral in Beckmann’s transformation and is parameterised to ensure the solution of the new problem satisfies Wardrop’s first principle of network equilibrium. It is shown that this method is equivalent to the variational inequality approach.

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Section: The Above Expression Is Clearly a Generalization Of The Obje...mentioning

confidence: 99%