Robustness analysis of multiprocessor schedules

Abstract

Tasks executing on general purpose multiprocessor platforms exhibit variations in their execution times. As such, there is a need to explicitly consider robustness, i.e., tolerance to these fluctuations. This work aims to quantify the robustness of schedules of directed acyclic graphs (DAGs) on multiprocessors by defining probabilistic robustness metrics and to present a new approach to perform robustness analysis to obtain these metrics. Stochastic execution times of tasks are used to compute completion time distributions which are then used to compute the metrics. To overcome the difficulties involved with the max operation on distributions, a new curve fitting approach is presented using which we can derive a distribution from a combination of analytical and limited simulation based results. The approach has been validated on schedules of time-critical applications in ASML wafer scanners.

The Impact of Deadline Misses on the Control Performance of High-End Motion Control Systems

“…2) can have different modes due to data losses, see (5). These mode switches are governed by the discrete-time stochastic process σ.…”

“…In the past decade traditional special-purpose platforms have been replaced by general-purpose multi-processor platforms [5], mainly due to reasons of cost and flexibility. This replacement leads to the introduction of significant variability in the task execution times [6, p. 12].…”

“…We model the occurrence of deadline misses by random variables resulting from the uncertainty in the execution times of real-time tasks [6, p. 249], [18]. Exploiting the techniques provided in [5], we can obtain the probability distribution of the completion times of control-related tasks. We assume that control-related tasks start to be processed immediately after new sensor measurements are acquired, which occurs at times {kh | k ∈ N}, where h is the sampling period.…”

Ant colony based constrained workflow scheduling for heterogeneous computing systems

“…As discussed before, the makespan or cost may be perturbed at runtime because of non-determinism in activities execution [21][22][23] and the dynamicity of performance of resources [15,25,26]. Regarding these factors, the robustness of the schedule at run-time is important.…”

“…First, the execution time of activities are nondeterministic [21][22][23][24]. The authors of [24] regard factors like input parameters to estimate the job execution time through simulation and the Amdahl's law.…”