Exact speedup factors and sub-optimality for non-preemptive scheduling

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 suboptimality 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.Preliminary publication: This paper extends initial research into speedup factors for preemptive versus non-preemptive uniprocessor scheduling published in RTSS 2015 (Davis et al. 2015c). The main extension is the proof of the exact speedup factor required to guarantee the FP-P feasibility of any FP-NP feasible constrained-deadline task set. Real-Time Syst (2018) 54:208-246 209 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 viceversa. 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.

An Improved Speedup Factor for Sporadic Tasks with Constrained Deadlines Under Dynamic Priority Scheduling

“…running jobs might be interrupted by emergent ones ), Global-EDF has a speedup factor 2−1/m [9] for scheduling set of tasks on m identical processors, and there is a polynomial-time algorithm for uniprocessors whose speedup factor is 1 + [10], where > 0 is sufficiently small for uniform processors, refer to [11]. For the non-preemptive case, there are also a variety of results, refer to [12], [13]. Except the speedup factor, there are many papers concerning about the utilization upper bound, refer to [14]- [16].…”