Linear model of traffic flow in an isolated network. (English) Zbl 1336.34087
Summary: 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 A related model which uses outdated information is shown to collapse in finite time.
MSC:
| 34K06 | Linear functional-differential equations |
| 34A30 | Linear ordinary differential equations and systems |
| 90B20 | Traffic problems in operations research |
References:
| [1] | J. K. Hale, <em>Theory of Functional Differential Equations</em>,, Springer-Verlag (1977) · Zbl 0352.34001 |
| [2] | J. K. Hale, <em>Dynamics in Infinite Dimensions</em>,, Springer-Verlag (2002) |
| [3] | A. Jiménez-Casas, A Model of Traffic Flow in a Network,, Advances in Differential Equations and Applications, 4, 193 (2014) |
| [4] | A. Jiménez-Casas, General model of traffic flow in an isolated network,, in preparation. · Zbl 1370.90041 |
| [5] | B. Sridhar, Comparison of Linear Dynamic Models for Air Traffic Flow Management,, Proceedings of the 16th IFAC World Congress, 1962 (2005) |
| [6] | D. Sun, 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, 569 (2007) · Zbl 1143.90006 |
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