Traffic plans

Marc BERNOT; Vicent CASELLES; Jean-Michel MOREL

doi:10.5565/PUBLMAT_49205_09

Traffic plans

Marc BERNOT^*
, Vicent CASELLES^*
, Jean-Michel MOREL^*

^*Corresponding author for this work

Research output: Journal Publications › Review article › Book review › peer-review

54 Citations (Scopus)

Abstract

In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure μ+ onto a measure μ- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,...) but it is no more realistic when we want to specify "who goes where", like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approaches and permitting to solve the optimal transport problem under the "who goes where" constraint. This constraint is formalized as a transference plan from μ+ to μ- which we handle as a boundary condition for the "optimal traffic problem".

Original language	English
Pages (from-to)	417-451
Number of pages	35
Journal	Publicacions Matematiques
Volume	49
Issue number	2
DOIs	https://doi.org/10.5565/PUBLMAT_49205_09
Publication status	Published - 2005
Externally published	Yes

Funding

We thank Professor Bernard Sapoval for valuable information, documentation and conversations. V. Caselles acknowledges partial support by the Departament d’Universitats, Recerca i Societat de la Informaci´o de la Generalitat de Catalunya and by PNPGC project, reference BFM2003-02125.

UN SDGs

This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 11 Sustainable Cities and Communities

Keywords

Irrigation
Traffic plan
Transference plan
Transport problem

Access to Document

10.5565/PUBLMAT_49205_09

Cite this

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title = "Traffic plans",

abstract = "In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure μ+ onto a measure μ- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,...) but it is no more realistic when we want to specify {"}who goes where{"}, like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approaches and permitting to solve the optimal transport problem under the {"}who goes where{"} constraint. This constraint is formalized as a transference plan from μ+ to μ- which we handle as a boundary condition for the {"}optimal traffic problem{"}.",

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AU - CASELLES, Vicent

AU - MOREL, Jean-Michel

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N2 - In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure μ+ onto a measure μ- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,...) but it is no more realistic when we want to specify "who goes where", like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approaches and permitting to solve the optimal transport problem under the "who goes where" constraint. This constraint is formalized as a transference plan from μ+ to μ- which we handle as a boundary condition for the "optimal traffic problem".

AB - In recent research in the optimization of transportation networks, the problem was formalized as finding the optimal paths to transport a measure μ+ onto a measure μ- with the same mass. This approach is realistic for simple good distribution networks (water, electric power,...) but it is no more realistic when we want to specify "who goes where", like in the mailing problem or the optimal urban traffic network problem. In this paper, we present a new framework generalizing the former approaches and permitting to solve the optimal transport problem under the "who goes where" constraint. This constraint is formalized as a transference plan from μ+ to μ- which we handle as a boundary condition for the "optimal traffic problem".

KW - Irrigation

KW - Traffic plan

KW - Transference plan

KW - Transport problem

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DO - 10.5565/PUBLMAT_49205_09

M3 - Review article

AN - SCOPUS:27444438520

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EP - 451

JO - Publicacions Matematiques

JF - Publicacions Matematiques

IS - 2

ER -

Traffic plans

Abstract

Funding

UN SDGs

Keywords

Access to Document

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