Quantifying the Sub-optimality of Non-preemptive Real-Time Scheduling

A number of preemptive real-time scheduling algorithms, such as Earliest Deadline First (EDF), are known to be optimal on uni-processor systems under specified assumptions. However, no uni-processor optimal algorithm exists under the non-preemptive scheduling paradigm. Hence preemptive schemes strictly dominate non-preemptive schemes with respect to uni-processor feasibility. However, the 'goodness' of non-preemptive schemes, compared to uni-processor optimal preemptive scheduling schemes such as EDF, which can also be referred to as its sub-optimality, has not been fully investigated yet. In this paper, we apply resource augmentation, specifically processor speed-up, to quantify the sub-optimality of non-preemptive scheduling with respect to EDF, and apply the results to guarantee user specified upper-bounds on the preemption related scheduling costs. In particular, we derive an upper bound on the minimum processor speed-up required to guarantee the non-preemptive feasibility of tasks that are deemed feasible under the preemptive EDF, and we prove that, in the cases where, for all tasks in the task set, the largest execution requirement is not greater than the shortest deadline, this bound is equal to 4. We also show how the proposed approach enables a system designer to choose an optimal processor, in order to, e.g., guarantee specified upper bounds on the preemption related overheads.