Article Contents
Article Contents

# Linear model of traffic flow in an isolated network

• 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 A related model which used outdated information is shown to collapse in finite time.
Mathematics Subject Classification: Primary: 34K06, 34A33; Secondary: 34A12, 34A30.

 Citation:

•  [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. [5] B. Sridhar and P. K. Menon, Comparison of Linear Dynamic Models for Air Traffic Flow Management, Proceedings of the 16th IFAC World Congress, (2005), 1962-1968. [6] D. Sun, I. S. Strub and A. M. Bayen, Comparison of the Performance of Four Eulerian Network Flow Models for Strategic Air Traffic Network Flow Models for Strategic Air Traffic Management, Networks and Heterogeneous Media, 2(4) (2007), 569-594.
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