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Personne# Denisa Gabriela Ghita

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Algorithme

thumb|Algorithme de découpe d'un polygone quelconque en triangles (triangulation).
Un algorithme est une suite finie et non ambiguë d'instructions et d’opérations permettant de résoudre une classe de

Topologie de réseau

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Une topologie de réseau informatique correspond à l'architecture (physique, logicielle ou logique) de celui-ci, définissant les liaisons entre les équipements du réseau et une hiérarchie éven

Réseau informatique

thumb|upright|Connecteurs RJ-45 servant à la connexion des réseaux informatiques via Ethernet.
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Un réseau informatique ( ou DCN) est un ensemble d'équipements reliés entre eux pour échan

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In this thesis, we investigate methods for the practical and accurate localization of Internet performance problems. The methods we propose belong to the field of network loss tomography, that is, they infer the loss characteristics of links from end-to-end measurements. The existing versions of the problem of network loss tomography are ill-posed, hence, tomographic algorithms that attempt to solve them resort to making various assumptions, and as these assumptions do not usually hold in practice, the information provided by the algorithms might be inaccurate. We argue, therefore, for tomographic algorithms that work under weak, realistic assumptions. We first propose an algorithm that infers the loss rates of network links from end-to-end measurements. Inspired by previous work, we design an algorithm that gains initial information about the network by computing the variances of links' loss rates and by using these variances as an indication of the congestion level of links, i.e., the more congested the link, the higher the variance of its loss rate. Its novelty lies in the way it uses this information – to identify and characterize the maximum set of links whose loss rates can be accurately inferred from end-to-end measurements. We show that our algorithm performs significantly better than the existing alternatives, and that this advantage increases with the number of congested links in the network. Furthermore, we validate its performance by using an "Internet tomographer" that runs on a real testbed. Second, we show that it is feasible to perform network loss tomography in the presence of "link correlations," i.e., when the losses that occur on one link might depend on the losses that occur on other links in the network. More precisely, we formally derive the necessary and sufficient condition under which the probability that each set of links is congested is statistically identifiable from end-to-end measurements even in the presence of link correlations. In doing so, we challenge one of the popular assumptions in network loss tomography, specifically, the assumption that all links are independent. The model we propose assumes we know which links are most likely to be correlated, but it does not assume any knowledge about the nature or the degree of their correlations. In practice, we consider that all links in the same local area network or the same administrative domain are potentially correlated, because they could be sharing physical links, network equipment, or even management processes. Finally, we design a practical algorithm that solves "Congestion Probability Inference" even in the presence of link correlations, i.e., it infers the probability that each set of links is congested even when the losses that occur on one link might depend on the losses that occur on other links in the network. We model Congestion Probability Inference as a system of linear equations where each equation corresponds to a set of paths. Because it is infeasible to consider an equation for each set of paths in the network, our algorithm finds the maximum number of linearly independent equations by selecting particular sets of paths based on our theoretical results. On the one hand, the information provided by our algorithm is less than that provided by the existing alternatives that infer either the loss rates or the congestion statuses of links, i.e., we only learn how often each set of links is congested, as opposed to how many packets were lost at each link, or to which particular links were congested when. On the other hand, this information is more useful in practice because our algorithm works under assumptions weaker than those required by the existing alternatives, and we experimentally show that it is accurate under challenging network conditions such as non-stationary network dynamics and sparse topologies.

Boolean Inference makes it possible to observe the congestion status of end-to-end paths and infer, from that, the congestion status of individual network links. In principle, this can be a powerful monitoring tool, in scenarios where we want to monitor a network without having direct access to its links. We consider one such real scenario: a Tier-1 ISP operator wants to monitor the congestion status of its peers. We show that, in this scenario, Boolean Inference cannot be solved with enough accuracy to be useful; we do not attribute this to the limitations of particular algorithms, but to the fundamental difficulty of the Inference problem. Instead, we argue that the ``right'' problem to solve, in this context, is compute the probability that each set of links is congested (as opposed to try to infer which particular links were congested when). Even though solving this problem yields less information than provided by Boolean Inference, we show that this information is more useful in practice, because it can be obtained accurately under weaker assumptions than typically required by Inference algorithms and more challenging network conditions (link correlations, non-stationary network dynamics, sparse topologies).

2011