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Networks and Heterogeneous Media

2007, Volume 2, Issue 3: 497-528. doi: 10.3934/nhm.2007.2.497
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Equilibria for data networks

  • 1.
    Dipartimento di Matematica "G. Castelnuovo", Università di Roma "La Sapienza", Viale del Policlinico 137, 00161 Rome
  • Received: 01 February 2007 Revised: 01 May 2007

  • Primary: 90B18; Secondary: 35L65.

  • This paper investigates equilibrium solutions for data flows on a network. We consider a fluid dynamic model based on conservation laws. The dynamics at nodes is solved by FIFO policy combined with through flux maximization. We first link the dimension of the equilibria space to topological properties of the graph associated to the network. Then we focus on regular plane tilings with square or triangular cells. For various networks, we completely determine the characteristics of periodic equilibria and, in some cases, of all equilibria. The obtained results are expected to play a role both in the analysis of asymptotic behavior of network load and for security issues in case of node failures.

    Citation: Alessia Marigo. Equilibria for data networks[J]. Networks and Heterogeneous Media, 2007, 2(3): 497-528. doi: 10.3934/nhm.2007.2.497

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  • This paper investigates equilibrium solutions for data flows on a network. We consider a fluid dynamic model based on conservation laws. The dynamics at nodes is solved by FIFO policy combined with through flux maximization. We first link the dimension of the equilibria space to topological properties of the graph associated to the network. Then we focus on regular plane tilings with square or triangular cells. For various networks, we completely determine the characteristics of periodic equilibria and, in some cases, of all equilibria. The obtained results are expected to play a role both in the analysis of asymptotic behavior of network load and for security issues in case of node failures.


  • This article has been cited by:

    1. Georges Bastin, Jean-Michel Coron, 2016, Chapter 3, 978-3-319-32060-1, 85, 10.1007/978-3-319-32062-5_3
    2. Zlatinka Dimitrova, Flows of Substances in Networks and Network Channels: Selected Results and Applications, 2022, 24, 1099-4300, 1485, 10.3390/e24101485
    3. Georges Bastin, Jean-Michel Coron, Exponential stability of networks of density-flow conservation laws under PI boundary control, 2013, 46, 14746670, 221, 10.3182/20130925-3-FR-4043.00029
    4. Georges Bastin, Jean-Michel Coron, Simona Oana Tamasoiu, Stability of linear density-flow hyperbolic systems under PI boundary control, 2015, 53, 00051098, 37, 10.1016/j.automatica.2014.12.025
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  • © 2007 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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