Linear model of traffic flow in an isolated network

Ángela Jiménez-Casas; Aníbal Rodríguez-Bernal

doi:10.3934/proc.2015.0670

Article Contents

2015, Volume 2015: 670-677. Doi: 10.3934/proc.2015.0670 open access

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Linear model of traffic flow in an isolated network

Ángela Jiménez-Casas^1, and
Aníbal Rodríguez-Bernal^2,

1.
Grupo de Dinámica No Lineal. Universidad Pontificia Comillas de Madrid, C/Alberto Agulilera 23, 28015 Madrid
2.
Departamento de Matemática Aplicada, Universidad Complutense de Madrid, 28040 Madrid

Received: August 31, 2014

Revised: March 31, 2015

Published: October 2015

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Abstract

We obtain a mathematical linear model which describes automatic operation of the traffic of material objects in a network. Existence and global solutions is obtained for such model. A related model which used outdated information is shown to collapse in finite time.

Keywords:

Mathematics Subject Classification: Primary: 34K06, 34A33; Secondary: 34A12, 34A30.

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References

[1]	J. K. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, (1977).
[2]	J. K. Hale, L. T. Magalhaes and W. M. Oliva, Dynamics in Infinite Dimensions, Springer-Verlag, New York, (2002).
[3]	A. Jiménez-Casas and A. Rodríguez-Bernal, A Model of Traffic Flow in a Network, Advances in Differential Equations and Applications, SEMA/SIMAI Springer Series, 4 (2014), 193-200, ISBN 978-3-319-06952-4.
[4]	A. Jiménez-Casas and A. Rodríguez-Bernal, General model of traffic flow in an isolated network, in preparation.
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