Column generation integer programming for allocating jobs with periodic demand variations

International audienceIn the context of service hosting in large-scale datacenters, we consider the problem faced by a provider for allocating services to machines. An analysis of a public Google trace corresponding to the use of a production cluster over a long period shows that long-running services experience demand variations with a periodic (daily) pattern, and that services with such a pattern account for most of the overall CPU demand. This leads to an allocation problem where the classical Bin-Packing issue is augmented with the possibility to co-locate jobs whose peaks occur at different times of the day, which is bound to be more efficient than the usual approach that consist in over-provisioning for the maximum demand. In this paper, we propose a column-generation approach to solving this problem, where the subproblem uses a sophisticated SOCP (Second Order Cone Program) formulation. This allows to explicitely select jobs which benefit from being co-allocated together. Experimental results comparing with theoretical lower bounds and with standard packing heuristics shows that this approach is able to provide very efficient assignments in reasonable time

Placement et ordonnancement statique et dynamique de tâches matérielles temps réel sur plateformes reconfigurables dynamiquement

The placement and scheduling of hardware tasks are the cores of the real-time operating system. Both problems must be solved efficiently to enhance the placement quality expressed by the rate of resource fragmentation and configuration overhead, and to improve the scheduling quality represented by the temporal spanning of the application and the guarantee of real-time constraints. In the context of the mixed architectures such as System on Programmable Chip (SoPC), we suggest exploiting the physical features of these architectures especially the partial run-time reconfiguration. The first part of the thesis deals with preemptive independents tasks. It suggests analytic resolution by means of mixed integer programming solver using the Branch and Bound method to achieve off-line placement of these tasks on a SoPC. The Bees metaheuristic is also proposed to handle this problem and we suggest employing dynamically the Earliest Deadline First algorithm to perform the real-time scheduling. The second part of the thesis focuses on dependent tasks where each one runs after the completion of all its proposed to resolve statically the placement and scheduling of periodic hardware tasks in a sole directed acyclic graph (DAG) on a SoPC. Four dynamic approaches are also proposed to place and schedule dynamically multiple DAGs with unknown behavior on several SoPCs. Basing on prefetch and reuse techniques, these approaches aim to reduce the temporal spanning of DAGs, and to improve the guarantee of real-time constraints and resource efficiency.Le placement et l ordonnancement des tâches matérielles sont les éléments clés du système d exploitation temps réel. Ces deux problèmes doivent être traités efficacement afin d améliorer la qualité du placement exprimée par le taux de fragmentation de ressources et la latence de reconfiguration, et la qualité d ordonnancement représentée par la durée d exécution de l application et la garantie des échéances. En utilisant les systèmes sur puce programmable, nous proposons d exploiter les caractéristiques physiques de ces puces, en particulier la reconfiguration partielle dynamique. Nous traitons, dans premier temps, les tâches indépendantes. Nous suggérons une résolution analytique par des solveurs de programmation en nombres entiers mixtes qui se basent sur la méthode de séparation et évaluation pour réaliser le placement hors-ligne de ces tâches sur puce. La métaheuristique des abeilles est aussi proposer pour traiter ce problème. Nous proposons d employer l algorithme Earliest deadline first pour construire l ordonnancement temps réel en ligne. Nous nous intéressons ensuite aux tâches dépendantes. En se basant également sur la programmation en nombres entiers mixtes, le placement et l ordonnancement statiques des tâches matérielles périodiques, constituant un graphe acyclique orienté, sont élaborés. Quatre approches dynamiques sont proposées pour effectuer le placement et l ordonnancement dynamique de plusieurs graphes sur différentes puces. Par les techniques de réutilisation et de prédiction, ces approches visent la réduction des temps d exécution des graphes, la garantie des échéances et l efficacité des ressources.NICE-BU Sciences (060882101) / SudocSudocFranceF

Column generation integer programming for allocating jobs with periodic demand variations

In the context of service hosting in large-scale datacenters, we consider the problem faced by a provider for allocating services to machines. An analysis of a public Google trace corresponding to the use of a production cluster over a long period shows that long-running services experience demand variations with a periodic (daily) pattern, and that services with such a pattern account for most of the overall CPU demand. This leads to an allocation problem where the classical Bin-Packing issue is augmented with the possibility to co-locate jobs whose peaks occur at different times of the day, which is bound to be more efficient than the usual approach that consist in over-provisioning for the maximum demand. In this paper, we propose a column-generation approach to solving this problem, where the subproblem uses a sophisticated SOCP (Second Order Cone Program) formulation. This allows to explicitely select jobs which benefit from being co-allocated together. Experimental results comparing with theoretical lower bounds and with standard packing heuristics shows that this approach is able to provide very efficient assignments in reasonable time.Simulation de systèmes de prochaine génératio

Static Scheduling of Periodic Hardware Tasks with Precedence and Deadline Constraints on Reconfigurable Hardware Devices

Task graph scheduling for reconfigurable hardware devices can be defined as finding a schedule for a set of periodic tasks with precedence, dependence, and deadline constraints as well as their optimal allocations on the available heterogeneous hardware resources. This paper proposes a new methodology comprising three main stages. Using these three main stages, dynamic partial reconfiguration and mixed integer programming, pipelined scheduling and efficient placement are achieved and enable parallel computing of the task graph on the reconfigurable devices by optimizing placement/scheduling quality. Experiments on an application of heterogeneous hardware tasks demonstrate an improvement of resource utilization of 12.45% of the available reconfigurable resources corresponding to a resource gain of 17.3% compared to a static design. The configuration overhead is reduced to 2% of the total running time. Due to pipelined scheduling, the task graph spanning is minimized by 4% compared to sequential execution of the graph

Allocating jobs with periodic demand variations

In the context of service hosting in large-scale datacenters, we consider the problem faced by a provider for allocating services to machines. Based on an analysis of a public Google trace correspond-ing to the use of a production cluster over a long period, we propose a model where long-running services experience demand variations with a periodic (daily) pattern and we prove that services following this model acknowledge for most of the overall CPU demand. This leads to an allo-cation problem where the classical Bin-Packing issue is augmented with the possibility to co-locate jobs whose peaks occur at different times of the day, which is bound to be more efficient than the usual approach that consist in over-provisioning for the maximum demand. In this paper, we provide a mathematical framework to analyze the packing of services exhibiting daily patterns and whose peaks occur at different times. We propose a sophisticated SOCP (Second Order Cone Program) formula-tion for this problem and we analyze how this modified packing constraint changes the behavior of standard packing heuristics (such as Best-Fit or First-Fit Decreasing). We show that taking periodicity of demand into account allows for a substantial improvement on machine utilization in the context of large-scale, state-of-the-art production datacenters.Simulation de systèmes de prochaine génératio