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Infrastructure adaptation and emergence of loops in network routing with time-dependent loads

Alessandro Lonardi1,*, Enrico Facca2, Mario Putti3, and Caterina De Bacco1,†

  • 1Max Planck Institute for Intelligent Systems, Cyber Valley, 72076 Tübingen, Germany
  • 2Laboratoire Paul Painlevé, UMR No. 8524, CNRS, Inria, Université Lille, 59000 Lille, France
  • 3Department of Mathematics “Tullio Levi-Civita,” University of Padua, Via Trieste 63, 35131 Padua, Italy

  • *alessandro.lonardi@tuebingen.mpg.de
  • †caterina.debacco@tuebingen.mpg.de
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Phys. Rev. E 107, 024302 – Published 3 February, 2023

DOI: https://doi.org/10.1103/PhysRevE.107.024302

Abstract

Network routing approaches are widely used to study the evolution in time of self-adapting systems. However, few advances have been made for problems where adaptation is governed by time-dependent inputs. In this work we study a dynamical systems where the edge conductivities of a network are regulated by time-varying mass loads injected on nodes. Motivated by empirical observations, we assume that conductivities adapt slowly with respect to the characteristic time of the loads. Furthermore, assuming the loads to be periodic, we derive a dynamics where the evolution of the system is controlled by a matrix obtained with the Fourier coefficients of the input loads. Remarkably, we find a sufficient condition on these coefficients that determines when the resulting network topologies are trees. We show an example of this on the Bordeaux bus network where we tune the input loads to interpolate between loopy and tree topologies. We validate our model on several synthetic networks and provide an expression for long-time solutions of the original conductivities.

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Phys. Rev. E 107, 024302– Published 3 February, 2023
  • Received 27 September 2022
  • Accepted 24 January 2023
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Open access publication funded by the Max Planck Society.

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