Making Speculative Scheduling Robust to Incomplete Data In this work, we study the robustness of Speculative Scheduling to data incompleteness. Speculative scheduling has allowed to incorporate future types of applications into the design of HPC schedulers, specifically applications whose runtime is not perfectly known but can be modeled with probability distributions. Preliminary studies show the importance of spec ulative scheduling in dealing with stochastic applications when the application runtime model is completely known. In this work we show how one can extract enough information even from incomplete behavioral data for a given HPC applications so that speculative scheduling still performs well. Specifically, we show that for synthetic runtimes who follow usual probability distributions such as truncated normal or exponential, we can extract enough data from as little as 10 previous runs, to be within 5% of the solution which has exact information. For real traces of applications, the performance with 10 data points varies with the applications (within 20% of the fullknowledge solution), but converges fast (5% with 100 previous samples). Finally a side effect of this study is to show the importance of the theoretical results obtained on continuous probability distributions for speculative scheduling. Indeed, we observe that the solutions for such distributions are more robust to incomplete data than the solutions for discrete distributions.

Schedulability analysis of dependent probabilistic realtime tasks The complexity of modern architectures has increased the timing variability of programs (or tasks). In this context, new approaches based on probabilistic methods are proposed to decrease the pessimism by associating probabilities to the worst case values of the programs (tasks) time execution. In this paper, we extend the original work of Chetto et al. 7 on precedence constrained tasks to the case of tasks with worst case execution times described by probability distributions. The precedence constraints between tasks are defined by acyclic directed graphs and these constraints are transformed in appropriate release times and deadlines. The new release times and deadlines are built using new maximum and minimum relations between pairs of probability distributions. We provide a probabilistic schedulability condition based on these new relations.