Optimization for a special class of traffic flow models: Combinatorial and continuous approaches

Göttlich, Simone; Kolb, Oliver; Kühn, Sebastian

doi:10.3934/nhm.2014.9.315

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Derivation Of the Mixed-integer Model1

Introduction1

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2015

2023

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Cited by 7 publications

(2 citation statements)

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“…These variables are equal to one if the density is smaller than or equal to ρ n i ; otherwise, they are zero. As proposed in [31], we reduce the number of constraints as follows: where ðκ t n;i Þ 2 ¼ κ t n;i . Analogously, we obtain…”

Section: Derivation Of the Mixed-integer Modelmentioning

confidence: 99%

Modeling and optimizing traffic light settings in road networks

Göttlich

Herty

Ziegler

2015

Computers & Operations Research

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Section: Derivation Of the Mixed-integer Modelmentioning

confidence: 99%

Modeling and optimizing traffic light settings in road networks

Göttlich

Herty

Ziegler

2015

Computers & Operations Research

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“…There are several applications where networks of hyperbolic conservation laws are involved, e.g., gas and water supply networks [6,12,23], traffic flow [5,9,15,17] or blood flow [26,27]. Those models mainly consist of one-dimensional domains on the edges of an underlying graph complemented with appropriate coupling and boundary conditions at the nodes of the network.…”

Section: Introductionmentioning

confidence: 99%

On a third order CWENO boundary treatment with application to networks of hyperbolic conservation laws

Naumann

Kolb

Semplice

2018

Applied Mathematics and Computation

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High order numerical methods for networks of hyperbolic conservation laws have recently gained increasing popularity. Here, the crucial part is to treat the boundaries of the single (one-dimensional) computational domains in such a way that the desired convergence rate is achieved in the smooth case but also stability criterions are fulfilled, in particular in the presence of discontinuities. Most of the recently proposed methods rely on a WENO extrapolation technique introduced by Tan and Shu in [J. Comput. Phys. 229, pp. 8144-8166 (2010)]. Within this work, we refine and in a sense generalize these results for the case of a third order scheme. Numerical evidence for the analytically found parameter bounds is given as well as results for a complete third order scheme based on the proposed boundary treatment.

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