Real-time scheduling algorithms proposed in the literature are often based onworst-case estimates of task parameters. The performance of an open-loop schemecan be degraded significantly if there are uncertainties in task parameters,such as the execution times of the tasks. Therefore, to cope with such asituation, a closed-loop scheme, where feedback is exploited to adjust thesystem parameters, can be applied. We propose an optimal control framework thattakes advantage of feeding back information of finished tasks to solve areal-time multiprocessor scheduling problem with uncertainty in task executiontimes, with the objective of minimizing the total energy consumption.Specifically, we propose a linear programming based algorithm to solve aworkload partitioning problem and adopt McNaughton's wrap around algorithm tofind the task execution order. The simulation results illustrate that ourfeedback scheduling algorithm can save energy by as much as 40% compared to anopen-loop method for two processor models, i.e. a PowerPC 405LP and an XScaleprocessor.
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