Robustness analysis of multiprocessor schedules

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.