Steady-State Scheduling of Task Graphs onto Heterogeneous Platforms

Matthieu Gallet 1, 2
1 GRAAL - Algorithms and Scheduling for Distributed Heterogeneous Platforms
Inria Grenoble - Rhône-Alpes, LIP - Laboratoire de l'Informatique du Parallélisme
Abstract : This thesis mainly deals with the mapping and the scheduling of applications on large heteroge- neous platforms. As the general scheduling problem is untractable, we consider two relaxations which apply to specific problems. Divisible load scheduling: Divisible loads are perfectly parallel applications, which can be split into chunks of arbitrary sizes to be distributed to many workers. We focus our attention on scheduling several divisible loads with different characteristics on linear networks of processors, in order to minimize the total processing time. This distribution may be done using several installments. Given a number of installments, we expose an algorithm giving an optimal dis- tribution of loads on processors, and we compare it to a pre-existing solution. Moreover, we show that any optimal distribution uses an infinite number of installments, leading to unfeasible solutions. This results also holds true for star-shaped platforms. Steady-state scheduling: In the second part, we discuss the issue of scheduling many copies of a given application, which is represented by a complex task graph. Instead of minimizing the completion time, we concentrate on the heart of the schedule and we try to maximize the throughput of the whole platform, without considering the start nor the end of our schedules. In this part, we first study the scheduling of complex but static applications, made of acyclic task graphs, on general heterogeneous platforms. To preserve a simple deployment of the application, produced schedules are made of a single allocation. Due to the NP-completeness of the problem, we not only provide an optimal solution, but also several heuristics returning efficient schedules. We compare our solutions to classical scheduling algorithms such as HEFT. In a second step, we focus on a collection of simpler but dynamic applications to schedule on fully heterogeneous master-workers platforms: the characteristics of their instances are varying. Designing static schedules taking care of this dynamicity is difficult, even in case of simple bag- of-tasks applications. Assuming that these variations are represented by random variables, we provide an ε-approximation in clairvoyant context and efficient heuristics for both the semi- clairvoyant and non-clairvoyant cases. We present many simulations to assess their qualities compared to the Round-Robin or the On-Demand policies. In a third step, we deal with pipeline applications, of which several tasks are replicated on different processors to increase the global throughput. In this case, even if instances are dis- tributed in a simple Round-Robin fashion and if the mapping is completely specified, computing the throughput of the platform is difficult. We expose a model based on Timed Petri Nets to compute them; we also prove that the throughput can be computed in polynomial time for the Strict One-Port communication model. Finally, steady-state techniques are effectively used to schedule complex task graph on a hetero- geneous multi-core processor, the IBM Cell. We present a theoretical model of this processor and an efficient algorithm to schedule many instances of complex task graphs. An complete implementation of this algorithm shows strong performances, while actual throughputs are very close to those predicted by our solution.
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Matthieu Gallet. Steady-State Scheduling of Task Graphs onto Heterogeneous Platforms. Modeling and Simulation. Ecole normale supérieure de lyon - ENS LYON, 2009. English. ⟨tel-00637362⟩



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