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Reactive Robust Routing: Anomaly Localization and Routing Reconfiguration for Dynamic Networks

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Abstract

This paper presents a novel approach to deal with dynamic and highly uncertain traffic in dynamic network scenarios. The Reactive Robust Routing (RRR) approach is introduced, a combination of proactive and reactive techniques to improve network efficiency and robustness, simplifying network operation. RRR optimizes routing for normal-operation traffic, using a time-varying extension of the already established Robust Routing technique that outperforms the stable approach. To deal with anomalous and unexpected traffic variations, RRR uses a fast anomaly detection and localization algorithm that rapidly detects and localizes abrupt changes in traffic flows, permitting an accurate routing adaptation. This algorithm presents well-established optimality properties in terms of detection/localization rates and localization delay, which allows for generalization of results, independently of particular evaluations. The algorithm is based on a novel parsimonious model for traffic demands which allows for detection of anomalies using easily available aggregated-traffic measurements, reducing the overheads of data collection.

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Authors and Affiliations

  1. Universidad de la República, J. Herrera y Reissig 565, CP 11300, Montevideo, Uruguay

    Pedro Casas

  2. ICD/LM2S, Université de Technologie de Troyes, 12 rue Marie Curie, BP 2060, 10010, Troyes Cedex, France

    Lionel Fillatre & Igor Nikiforov

  3. Télécom Bretagne, Technopôle Brest-Iroise, CS 83818, 29238, Brest Cedex 3, France

    Sandrine Vaton

Authors
  1. Pedro Casas
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  2. Lionel Fillatre
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  3. Sandrine Vaton
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  4. Igor Nikiforov
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Corresponding author

Correspondence to Pedro Casas.

Appendix: Elimination of the Anomaly-free Traffic

Appendix: Elimination of the Anomaly-free Traffic

The anomaly-free traffic \(H\varvec{\mu}_t\) is removed by projecting the whitened measurements vector \({\bf z}_t = \Upphi^{-\frac{1}{2}}{\bf y}_t\) onto the left null space of H (i.e. WH = 0). Let us define the matrix W T = (w 1, .., w r-q) of size r × (r − q), composed of eigenvectors w 1, .., w r-q of the projection matrix \(P_H^{\bot} = I_r - H{\left(H^TH\right)}^{-1}H^T\), corresponding to eigenvalue 1. The matrix W satisfies the following conditions: \(WH = 0, W^TW = P_H^{\bot}\), and WW T = I r-q. The matrix W can be considered as a linear rejector that eliminates the anomaly-free traffic. In the presence of an anomaly in OD flow j, traffic residuals u t  = W z t can be modeled as \({\bf u}_t = \theta W \Upphi^{-\frac{1}{2}} {\bf r}_j + W\varvec{\epsilon}_t\). By defining the vectors \({\bf v}_j=W\Upphi^{-\frac{1}{2}} {\bf r}_j\), we get the following distribution for traffic residuals in the presence of an anomaly in OD flow \(j: {\bf u}_t \sim {\mathcal N}(\theta {\bf v}_j,I_{r-q})\).

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Casas, P., Fillatre, L., Vaton, S. et al. Reactive Robust Routing: Anomaly Localization and Routing Reconfiguration for Dynamic Networks. J Netw Syst Manage 19, 58–83 (2011). https://doi.org/10.1007/s10922-010-9182-9

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  • DOI: https://doi.org/10.1007/s10922-010-9182-9

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