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A Model of Traffic Flow in a Network

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Advances in Differential Equations and Applications

Part of the book series: SEMA SIMAI Springer Series ((SEMA SIMAI,volume 4))

Abstract

We obtain a mathematical model which governs the traffic flow of material objects in a net to generalize several previous models like air traffic (Sridhar, Menon (2005) Comparison of linear dynamic models for air traffic flow management. IFAC, Prague; Sun, Strub, Bayen (2007) Netw Heterog Media 2(4):569–594). We analyze the existence and uniqueness of solutions for some particular case.

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References

  1. Arino, O., Sanchez, E.: Linear theory of abstract functional differential equations of retarded type. J. Math. Anal. Appl. 191, 547–571 (1995)

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  2. Hale, J.K., Magalhaes, L.T., Oliva, W.M.: Dynamics in Infinite Dimensions. Springer, New York (2002)

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  3. Sridhar, B., Menon, P.K.: Comparison of Linear Dynamic Models for Air Traffic Flow Management. Proceedings of the 16th IFAC World Congress, 1962–1968 (2005)

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  4. Sun, D., Strub, I.S., Bayen, A.M.: Comparison of the performance of four Eulerian network flow models for strategic air traffic network flow models for strategic air traffic management. Netw. Heterog. Media. 2(4), 569–594 (2007)

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Acknowledgements

Partially supported by grant MTM2012-31298 from Ministerio de Economia y Competitividad, Spain, GR58/08 Grupo 920894 BSCH-UCM, Grupo de Investigación CADEDIF and by Project FIS2009-12964-C05-03, SPAIN.

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Authors and Affiliations

  1. Departamento de Matemática Aplicada, Escuela Técnica Superior de Ingeniería (ICAI), Universidad Pontificia Comillas de Madrid, Calle de Alberto Aguilera 25, E-28015, Madrid, Spain

    Ángela Jiménez-Casas

  2. Departamento de Matemática Aplicada, Universidad Complutense de Madrid, E-28040, Madrid, Spain

    Aníbal Rodríguez-Bernal

  3. Instituto de Ciencias Matemáticas, CSIC-UAM-UC3M-UCM, E-28049, Madrid, Spain

    Aníbal Rodríguez-Bernal

Authors
  1. Ángela Jiménez-Casas
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  2. Aníbal Rodríguez-Bernal
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Corresponding author

Correspondence to Ángela Jiménez-Casas .

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Editors and Affiliations

  1. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Fernando Casas

  2. Dept. de Mathemàtiques and IMAC, Universitat Jaume I, Castelló, Spain

    Vicente Martínez

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Jiménez-Casas, Á., Rodríguez-Bernal, A. (2014). A Model of Traffic Flow in a Network. In: Casas, F., Martínez, V. (eds) Advances in Differential Equations and Applications. SEMA SIMAI Springer Series, vol 4. Springer, Cham. https://doi.org/10.1007/978-3-319-06953-1_19

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