Open Archive Toulouse Archive OuverteOATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible To cite this version: CauxAbstract. Nowadays, datacenters are one of the most energy consuming facilities due to the increase of cloud, web-services and high performance computing demands all over the world. To be clean and to be with no connection to the grid, datacenters projects try to feed electricity with renewable energy sources and storage elements. Nevertheless, due to the intermittent nature of these power sources, most of the works still rely on grid as a backup. This paper presents a model that considers the datacenter workload and the several moments where renewable energy could be engaged by the power side without grid. We propose to optimize the IT scheduling to execute tasks within a given power envelope of only renewable energy as a constraint.

Abstract:In this paper, we aim at minimizing the energy consumption when executing a divisible workload under a bound on the total execution time, while resilience is provided through checkpointing. We discuss several variants of this multi-criteria problem. Given the workload, we need to decide how many chunks to use, what are the sizes of these chunks, and at which speed each chunk is executed. Furthermore, since a failure may occur during the execution of a chunk, we also need to decide at which speed a chunk should be re-executed in the event of a failure. The goal is to minimize the expectation of the total energy consumption, while enforcing a deadline on the execution time, that should be met either in expectation (soft deadline), or in the worst case (hard deadline). For each problem instance, we propose either an exact solution, or a function that can be optimized numerically. The different models are then compared through an extensive set of experiments. Protocoles de checkpointà faible consommatioń energétique pour des tâches divisibles, sous contrainte faible ou forte du temps d'exécution Résumé :Ce travail viseà minimiser la consommation d'énergie lors de l'exécution d'une quantité de travail divisible, sous contrainte de temps d'exécution, sur une plateforme soumiseà des fautes passagères. La résilience est fournie grâceà un protocole de sauvegarde de points de reprise (checkpoints). Nousétudions différentes variantes de ce problème multi-critère. Etant donnée une quantité de travail, nous devons décider du découpage optimal de celle-ci en morceaux qui seront sauvegardés ; plus précisément, nous devons déterminer le nombre, la taille et la vitesse d'exécution de chacun de ces morceaux. De plus, sachant qu'une faute peut arriver pendant l'exécution de l'un d'entre eux, nous devons décider de la vitesse de ré-exécution de ces morceaux en cas de faute. Le but de ce travail est de minimiser l'espérance de la consommation d'énergie, sous une contrainte temporelle, qui peutêtre atteinte en moyenne (contrainte faible), ou dans le pire cas (contrainte forte). Pour chaque instance du problème, nous fournissons soit une solution exacte, soit une fonction qui peutêtre optimisée numériquement. Les différents modèles sont ensuite comparés via un ensemblé etendu d'expériences.

This paper deals with optimal strategies to place replicas in tree networks, with the double objective to minimize the total cost of the servers, and/or to optimize power consumption. The client requests are known beforehand, and some servers are assumed to pre-exist in the tree. Without power consumption constraints, the total cost is an arbitrary function of the number of existing servers that are reused, and of the number of new servers. Whenever creating and operating a new server has higher cost than reusing an existing one (which is a very natural assumption), cost optimal strategies have to tradeoff between reusing resources and load-balancing requests on new servers. We provide an optimal dynamic programming algorithm that returns the optimal cost, thereby extending known results without pre-existing servers. With power consumption constraints, we assume that servers operate under a set of M different modes depending upon the number of requests that they have to process. In practice M is a small number, typically 2 or 3, depending upon the number of allowed voltages. Power consumption includes a static part, proportional to the total number of servers, and a dynamic part, proportional to a constant exponent of the server mode, which depends upon the model for power. The cost function becomes a more complicated function that takes into account reuse and creation as before, but also upgrading or downgrading an existing server from one mode to another. We show that with an arbitrary number of modes, the power minimization problem is NP-complete, even without cost constraint, and without static power. Still, we provide an optimal dynamic programming algorithm that returns the minimal power, given a threshold value on the total cost; it has exponential complexity in the number of modes M , and its practical usefulness is limited to small values of M . Still, experiments conducted with this algorithm show that it can process large trees in reasonable time, despite its worst-case complexity.

In this paper, we study the problem of finding optimal mappings for several independent but concurrent workflow applications, in order to optimize performance-related criteria together with energy consumption. Each application consists in a linear chain application with several stages, and processes successive data sets in pipeline mode, from the first to the last stage. We study the problem complexity on different target execution platforms, ranking from fully homogeneous platforms to fully heterogeneous ones. The goal is to select an execution speed for each processor, and then to assign stages to processors, with the aim of optimizing several concurrent optimization criteria. There is a clear trade-off to reach, since running faster and/or more processors leads to better performance, but the energy consumption is then very high. Energy savings can be done at the price of a lower performance, by reducing processor speeds or enrolling fewer resources.. We consider two mapping strategies: in one-to-one mappings, a processor is assigned a single stage, while in interval mappings, a processor may process an interval of consecutive stages of the same application. For both mapping strategies and all platform types, we establish the complexity of several multi-criteria optimization problems, whose objective functions combine period, latency and energy criteria. In particular, we exhibit cases where the problem is NP-hard with concurrent applications, while it can be solved in polynomial time for a single application. Also, we demonstrate the difficulty of performance/energy trade-offs by proving that the tri-criteria problem is NP-hard, even with a single application on a fully homogeneous platform.