Abstract
Fixed priority scheduling is used in many real-time systems; however, both preemptive and non-preemptive variants (FP-P and FP-NP) are known to be sub-optimal when compared to an optimal uniprocessor scheduling algorithm such as preemptive earliest deadline first (EDF-P). In this paper, we investigate the sub-optimality of fixed priority non-preemptive scheduling. Specifically, we derive the exact processor speed-up factor required to guarantee the feasibility under FP-NP (i.e. schedulability assuming an optimal priority assignment) of any task set that is feasible under EDF-P. As a consequence of this work, we also derive a lower bound on the sub-optimality of non-preemptive EDF (EDF-NP). As this lower bound matches a recently published upper bound for the same quantity, it closes the exact sub-optimality for EDF-NP. It is known that neither preemptive, nor non-preemptive fixed priority scheduling dominates the other, in other words, there are task sets that are feasible on a processor of unit speed under FP-P that are not feasible under FP-NP and vice-versa. Hence comparing these two algorithms, there are non-trivial speedup factors in both directions. We derive the exact speed-up factor required to guarantee the FP-NP feasibility of any FP-P feasible task set. Further, we derive the exact speed-up factor required to guarantee FP-P feasibility of any constrained-deadline FP-NP feasible task set.
Highlights
Real-time systems are prevalent in a wide variety of application areas including telecommunications, consumer electronics, aerospace systems, automotive electronics, robotics, and medical systems
Theorem 2 The exact speedup factor required such that fixed priority non-preemptive scheduling (FP-NP), using optimal priority assignment, can schedule any implicit, or constrained-deadline sporadic task set that is feasible under fixed priority preemptive (FP-P) scheduling is given by: Proof Proof follows from the lower bound given by Lemma 3 and the upper bound given by Lemma 4 which have the same value
Proof Follows from Theorems 8, 9, and 10, and the fact that the bound so obtained using a necessary test for FP-NP scheduling assuming optimal priority assignment (OPA) compared to an exact test for FP-P assuming exactly the same priority ordering that FP-NP uses, is an upper bound for the general case described in the theorem
Summary
Real-time systems are prevalent in a wide variety of application areas including telecommunications, consumer electronics, aerospace systems, automotive electronics, robotics, and medical systems. One way of reducing or eliminating CRPD is to partition the cache; allocating each task a cache partition, which is some fraction of the overall size of the cache, has an impact on the task’s worst-case execution time (WCET) which may be significantly inflated Such partitioning rarely improves upon schedulability compared to accounting for CRPD and allowing tasks to use the entire cache (Altmeyer et al 2014, 2016). Task sets exist that are feasible under FP-NP that are not feasible under FP-P and vice-versa1 This lack of any dominance relationship means that when fixed priorities are used, some systems are easier to schedule preemptively, while others are easier to schedule non-preemptively.
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