Computational Complexity and Speedup Factors Analyses for Self-Suspending Tasks

Abstract

In computing systems, an execution entity (job/process/task) may suspend itself when it has to wait for some activities to continue/finish its execution. For real-time embedded systems, such self-suspending behavior has been shown to cause substantial performance/schedulability degradation in the literature. There are two commonly adopted self-suspending sporadic task models in real-time systems: 1) dynamic self-suspension and 2) segmented self-suspension sporadic task models. A dynamic self-suspending sporadic task is specified with an upper bound on the maximum suspension time for a job (task instance), which allows a job to dynamically suspend itself as long as the suspension upper bound is not violated. By contrast, a segmented self-suspending sporadic task has a predefined execution and suspension pattern in an interleaving manner.Even though some seemingly positive results have been reported for self-suspending task systems, the computational complexity and the theoretical quality (with respect to speedup factors) of fixed-priority preemptive scheduling have not been reported. This paper proves that the schedulability analysis for fixed-priority preemptive scheduling even with only one segmented self-suspending task as the lowest-priority task is coNP-hard in the strong sense. For dynamic self-suspending task systems, we show that the speedup factor for any fixed-priority preemptive scheduling, compared to the optimal schedules, is not bounded by a constant or by the number of tasks, if the suspension time cannot be reduced by speeding up. Such a statement of unbounded speedup factors can also be proved for earliest-deadline-first (EDF), least-laxity-first (LLF), and earliest-deadline-zero-laxity (EDZL) scheduling algorithms. However, if the suspension time can be reduced by speeding up coherently or the suspension time of each task is not comparable with (i.e., sufficiently smaller than) its relative deadline, then we successfully show that rate-monotonic scheduling has a constant speedup factor, with respect to the optimal schedules, for implicit-deadline task systems.