Federated scheduling for stochastic parallel real-time tasks

Federated scheduling is a strategy to schedule parallel real-time tasks: It allocates a dedicated cluster of cores to each high-utilization task (utilization ≥ 1); It uses a multiprocessor scheduling algorithm to schedule and execute all low-utilization tasks sequentially, on a shared cluster of the remaining cores. Prior work has shown that federated scheduling has the best known capacity augmentation bound of 2 for parallel tasks with implicit deadlines. In this paper, we explore the soft real-time performance of federated scheduling and address average-case workloads instead of worst-case ones. In particular, we consider stochastic tasks - tasks for which execution time and critical-path length are random variables. In this case, we use bounded expected tardiness as the schedulability criterion. We define a stochastic capacity augmentation bound and prove that federated scheduling algorithms guarantee the same bound of 2 for stochastic tasks. We present three federated mapping algorithms with different complexities for core allocation. All of them guarantee bounded expected tardiness and provide the same capacity augmentation bound. In practice, however, we expect them to provide different performance, both in terms of the task sets they can schedule and the actual tardiness they guarantee. Therefore, we present numerical evaluations using randomly generated task sets to examine the practical differences between the three algorithms.