A study of scheduling problems with preemptions on multi-core computers with GPU accelerators

International audienceFor many years, scheduling problems have been concerned either with parallel processor systems or with dedicated processors-job shop type systems. With a development of new computing architectures this partition is no longer so obvious. Multi-core (processor) computers equipped with GPU co-processors require new scheduling strategies. This paper is devoted to a characterization of this new type of scheduling problems. After a thorough introduction of the new model of a computing system, an extension of the classical notation of scheduling problems is proposed. A special attention is paid to preemptions, since this feature of the new architecture differs the most as compared with the classical model. In the paper, several scheduling algorithms, new ones and those refining classical approaches, are presented. Possible extensions of the model are also discussed

Algorithms for Hierarchical and Semi-Partitioned Parallel Scheduling

We propose a model for scheduling jobs in a parallel machine setting that takes into account the cost of migrations by assuming that the processing time of a job may depend on the specific set of machines among which the job is migrated. For the makespan minimization objective, the model generalizes classical scheduling problems such as unrelated parallel machine scheduling, as well as novel ones such as semi-partitioned and clustered scheduling. In the case of a hierarchical family of machines, we derive a compact integer linear programming formulation of the problem and leverage its fractional relaxation to obtain a polynomial-time 2-approximation algorithm. Extensions that incorporate memory capacity constraints are also discussed

A survey of offline algorithms for energy minimization under deadline constraints

Modern computers allow software to adjust power management settings like speed and sleep modes to decrease the power consumption, possibly at the price of a decreased performance. The impact of these techniques mainly depends on the schedule of the tasks. In this article, a survey on underlying theoretical results on power management, as well as offline scheduling algorithms that aim at minimizing the energy consumption under real-time constraints, is given

Real-time scheduling with resource sharing on heterogeneous multiprocessors

Consider the problem of scheduling a task set τ of implicit-deadline sporadic tasks to meet all deadlines on a t-type heterogeneous multiprocessor platform where tasks may access multiple shared resources. The multiprocessor platform has m k processors of type-k, where k∈{1,2,…,t}. The execution time of a task depends on the type of processor on which it executes. The set of shared resources is denoted by R. For each task τ i , there is a resource set R i ⊆R such that for each job of τ i , during one phase of its execution, the job requests to hold the resource set R i exclusively with the interpretation that (i) the job makes a single request to hold all the resources in the resource set R i and (ii) at all times, when a job of τ i holds R i , no other job holds any resource in R i . Each job of task τ i may request the resource set R i at most once during its execution. A job is allowed to migrate when it requests a resource set and when it releases the resource set but a job is not allowed to migrate at other times. Our goal is to design a scheduling algorithm for this problem and prove its performance. We propose an algorithm, LP-EE-vpr, which offers the guarantee that if an implicit-deadline sporadic task set is schedulable on a t-type heterogeneous multiprocessor platform by an optimal scheduling algorithm that allows a job to migrate only when it requests or releases a resource set, then our algorithm also meets the deadlines with the same restriction on job migration, if given processors 4×(1+MAXP×⌈|P|×MAXPmin{m1,m2,…,mt}⌉) times as fast. (Here MAXP and |P| are computed based on the resource sets that tasks request.) For the special case that each task requests at most one resource, the bound of LP-EE-vpr collapses to 4×(1+⌈|R|min{m1,m2,…,mt}⌉). To the best of our knowledge, LP-EE-vpr is the first algorithm with proven performance guarantee for real-time scheduling of sporadic tasks with resource sharing on t-type heterogeneous multiprocessors

Solving a multiprocessor problem by column generation and branch-and-price

This work presents an algorithm for solving exactly a scheduling problem with identical parallel machines and malleable tasks, subject to arbitrary release dates and due dates. The objective is to minimize a function of late work and setup costs. A task is malleable if we can freely change the set of machines assigned to its processing over the time horizon. We present an integer programming model, a Dantzig-Wolfe decomposition reformulation and its solution by column generation. We also developed an equivalent network flow model, used for the branching phase. Finally, we carried out extensive computational tests to verify the algorithm’s efficiency and to determine the model’s sensitivity to instance size parameters: the number of machines, the number of tasks and the size of the planning horizon

Idle regulation in non-clairvoyant scheduling of parallel jobs

AbstractThe optimization of parallel applications is difficult to achieve by classical optimization techniques because of their diversity and the variety of actual parallel and distributed platforms and/or environments. Adaptive algorithmic schemes, capable of dynamically changing the allocation of jobs during the execution to optimize global system behavior, are the best alternatives for solving this problem. In this paper, we focus on non-clairvoyant scheduling of parallel jobs with known resource requirements but unknown running times, with emphasis on the regulation of idle periods in the context of general list policies. We consider a new family of scheduling strategies based on two phases which successively combine sequential and parallel execution of jobs. We generalize known worst-case performance bounds by considering two extra parameters, in addition to the number of processors and maximum processor requirements considered in the literature, namely, job parallelization penalty and idle regulation factor. Furthermore, we prove that under certain conditions of idle regulation, the performance guarantee of parallel job scheduling in space-sharing mode can be improved

Control techniques for thermal-aware energy-efficient real time multiprocessor scheduling

La utilización de microprocesadores multinúcleo no sólo es atractiva para la industria sino que en muchos ámbitos es la única opción. La planificación tiempo real sobre estas plataformas es mucho más compleja que sobre monoprocesadores y en general empeoran el problema de sobre-diseño, llevando a la utilización de muchos más procesadores /núcleos de los necesarios. Se han propuesto algoritmos basados en planificación fluida que optimizan la utilización de los procesadores, pero hasta el momento presentan en general inconvenientes que los alejan de su aplicación práctica, no siendo el menor el elevado número de cambios de contexto y migraciones.Esta tesis parte de la hipótesis de que es posible diseñar algoritmos basados en planificación fluida, que optimizan la utilización de los procesadores, cumpliendo restricciones temporales, térmicas y energéticas, con un bajo número de cambios de contexto y migraciones, y compatibles tanto con la generación fuera de línea de ejecutivos cíclicos atractivos para la industria, como de planificadores que integran técnicas de control en tiempo de ejecución que permiten la gestión eficiente tanto de tareas aperiódicas como de desviaciones paramétricas o pequeñas perturbaciones.A este respecto, esta tesis contribuye con varias soluciones. En primer lugar, mejora una metodología de modelo que representa todas las dimensiones del problema bajo un único formalismo (Redes de Petri Continuas Temporizadas). En segundo lugar, propone un método de generación de un ejecutivo cíclico, calculado en ciclos de procesador, para un conjunto de tareas tiempo real duro sobre multiprocesadores que optimiza la utilización de los núcleos de procesamiento respetando también restricciones térmicas y de energía, sobre la base de una planificación fluida. Considerar la sobrecarga derivada del número de cambios de contexto y migraciones en un ejecutivo cíclico plantea un dilema de causalidad: el número de cambios de contexto (y en consecuencia su sobrecarga) no se conoce hasta generar el ejecutivo cíclico, pero dicho número no se puede minimizar hasta que se ha calculado. La tesis propone una solución a este dilema mediante un método iterativo de convergencia demostrada que logra minimizar la sobrecarga mencionada.En definitiva, la tesis consigue explotar la idea de planificación fluida para maximizar la utilización (donde maximizar la utilización es un gran problema en la industria) generando un sencillo ejecutivo cíclico de mínima sobrecarga (ya que la sobrecarga implica un gran problema de los planificadores basados en planificación fluida).Finalmente, se propone un método para utilizar las referencias de la planificación fuera de línea establecida en el ejecutivo cíclico para su seguimiento por parte de un controlador de frecuencia en línea, de modo que se pueden afrontar pequeñas perturbaciones y variaciones paramétricas, integrando la gestión de tareas aperiódicas (tiempo real blando) mientras se asegura la integridad de la ejecución del conjunto de tiempo real duro.Estas aportaciones constituyen una novedad en el campo, refrendada por las publicaciones derivadas de este trabajo de tesis.<br /