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Modèles markoviens de transfert de charge dans les réseaux informatiques

Abstract : The aim of this thesis is to model and to evaluate load transferring algorithms in parallel and/or distributed systems. After a synthesis of the different possible approaches of this load transfer and the main problems one gets both to install and to evaluate them with quantitative analysis, we study some models based on a Markovian evolution of the map of the total load of the whole set of processors. The performance indexes under consideration , in order to compare the values with and without transfer, are the memory saturation, the throughput, the workload and the mean response time. In the first two models, only two sites can transfer tasks on each other, but the communication and the transfer delays are taken into account. Critical values about accuracy or not of the transfer are obtained. When the communication and the transfer delays are negligible in front of the computation delays, two models are studied. The first one allows to evaluate a global load balancing algorithm for any number of sites fully connected, with finite memory capacity. This study yields the asymptotic behavior of massively parallel systems and upperbounds of some benefits that one can expect from a real transfer are derived. The second one takes into account the architecture of the net and the algorithm assumes that transfers occur between neighboring processors as soon as the load difference between them exceeds one. In the case of infinite lattice the model is proved to be ergodic and to converge exponentially fast to its equilibrium. Experimental results for different types of architectures are presented and compared to the solution of the mean field equations, that turn out in most cases to give fairly good approximation to the quantities of practical interest. Incidences of this politic of transfer on the values of the performance indexes are presented.
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Submitted on : Friday, February 20, 2004 - 10:05:22 AM
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  • HAL Id : tel-00004914, version 1



Maryse Y. Beguin. Modèles markoviens de transfert de charge dans les réseaux informatiques. Modélisation et simulation. Université Joseph-Fourier - Grenoble I, 1997. Français. ⟨tel-00004914⟩



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