Scheduling multiple divisible loads on a linear processor network

Min, Veeravalli, and Barlas have recently proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments. We show on a very simple example that their approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal schedule for any instance, once the number of installments per load is given. Then, we formally state that any optimal schedule has an infinite number of installments under a linear cost model as the one assumed in the original papers. Therefore, such a cost model cannot be used to design practical multi-installment strategies. Finally, through extensive simulations we confirmed that the best solution is always produced by the linear programming approach, while solutions of the original papers can be far away from the optimal

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Min, Veeravalli, and Barlas proposed strategies to minimize the overall execution time of one or several divisible loads on a heterogeneous linear network, using one or more installments. We show on a very simple example that the proposed approach does not always produce a solution and that, when it does, the solution is often suboptimal. We also show how to find an optimal scheduling for any instance, once the number of installments per load is given. Finally, we formally prove that under a linear cost model, as in the original paper, an optimal schedule has an infinite number of installments. Such a cost model can therefore not be sed to design practical multi-installment strategies

Scheduling divisible loads with time and cost constraints

In distributed computing, divisible load theory provides an important system model for allocation of data-intensive computations to processing units working in parallel. The main task is to define how a computation job should be split into parts, to which processors those parts should be allocated and in which sequence. The model is characterized by multiple parameters describing processor availability in time, transfer times of job parts to processors, their computation times and processor usage costs. The main criteria are usually the schedule length and cost minimization. In this paper, we provide the generalized formulation of the problem, combining key features of divisible load models studied in the literature, and prove its NP-hardness even for unrestricted processor availability windows. We formulate a linear program for the version of the problem with a fixed number of processors. For the case with an arbitrary number of processors, we close the gaps in the study of special cases, developing efficient algorithms for single criterion and bicriteria versions of the problem, when transfer times are negligible

Independent and Divisible Task Scheduling on Heterogeneous Star-shaped Platforms with Limited Memory

In this paper, we consider the problem of allocating and scheduling a collection of independent, equal-sized tasks on heterogeneous star-shaped platforms. We also address the same problem for divisible tasks. For both cases, we take memory constraints into account. We prove strong NP-completeness results for different objective functions, namely makespan minimization and throughput maximization, on simple star-shaped platforms. We propose an approximation algorithm based on the unconstrained version (with unlimited memory) of the problem. We introduce several heuristics, which are evaluated and compared through extensive simulations. An unexpected conclusion drawn from these experiments is that classical scheduling heuristics that try to greedily minimize the completion time of each task are outperformed by the simple heuristic that consists in assigning the task to the available processor that has the smallest communication time, regardless of computation power (hence a "bandwidth-centric" distribution).Dans ce rapport, nous nous intéressons au problème de l’allocation d’un grand nombre de taches indépendantes et de taille identiques sur des plateformes de calcul hétérogènes organisées en étoile. Nous nous intéressons également au modèle des tâches divisibles. Pour ces deux modèles, nous prenons en compte les contraintes mémoires et démontrons des résultats de NP-complétude pour diverses métriques (le «makespakan» et le débit). Nous proposons un algorithme d’approximation basé sur la version non-contrainte (c’est-`a-dire avec une mémoire infinie) du problème. Nous proposons également d’autres heuristiques que nous évaluons à l’aide d’un grand nombre de simulations. Une conclusion inattendue qui ressort de ces expériences est que les heuristiques de listes classiques qui essaient de minimiser gloutonnement la durée de l’ordonnancement sont bien moins performantes que l’heuristique toute simple consistant à envoyer les tâches aux processeurs disponibles ayant le temps de communication le plus faible, sans même tenir compte de leur puissance de calcu

Real-Time Divisible Load Scheduling with Different Processor Available Times

Providing QoS and performance guarantees to arbitrarily divisible loads has become a significant problem for many cluster-based research computing facilities. While progress is being made in scheduling arbitrarily divisible loads, some of proposed approaches may cause Inserted Idle Times (IITs) that are detrimental to system performance. In this paper we propose a new approach that utilizes IITs and thus enhances the system performance. The novelty of our approach is that, to simplify the analysis, a homogenous system with IITs is transformed to an equivalent heterogeneous system, and that our algorithms can schedule real-time divisible loads with different processor available times. Intensive simulations show that the new approach outperforms the previous approach in all configurations. We also compare the performance of our algorithm to the current practice of manually splitting workloads by users. Simulation results validate the advantages of our approach