Elastic scheduling of parallel real-time tasks with discrete utilizations

Elastic scheduling allows for online adaptation of real-time tasks' utilizations (via manipulation of each task's computational workload or period) in order to maintain system schedulability in case the utilization demand of one or more tasks changes. This is done currently by assigning each task a utilization (and therefore period or workload) from within a continuous range of acceptable values. While this works well for anytime tasks whose quality of service improves with duration or for tasks that can run at any rate within a given range, many computationally-elastic tasks have a specific workload for each distinct mode of operation and therefore cannot perform arbitrary amounts of work. Similarly, some period-elastic tasks must run at specific (e.g. harmonic) rates. Therefore, a discrete set of candidate utilizations per task must be accommodated in such cases. This paper provides a new elastic task model in which each task has a discrete set of possible utilizations (instead of a continuous range). This allows users to specify only relevant candidate periods and workloads for each task. The discrete nature of this model also allows each task to modify its workload and/or its period when changing its mode of operation, instead of adapting in only one dimension of task utilization. Elastic tasks thus can exploit both period elasticity and computational elasticity. This greatly increases both the diversity of adaptations available to each task and the kinds of real-time tasks relevant to elastic scheduling. We use the real-world example of real-time hybrid simulation as a motivating application domain with discretely computationally-elastic, period-elastic, and combined-elastic parallel real-time tasks under the Federated Scheduling paradigm. We prove the scheduling of these tasks to be NP-hard, and provide a pseudo-polynomial time scheduling algorithm. We then use this scheduling algorithm to implement the first virtual real-time hybrid simulation experiment in which discrete elastic adaptation of platform resource utilizations enables adaptive switching between controllers with differing computational demands. We also study the effects of scheduling tasks with discretized vs. continuous candidate utilizations.