Improved schedulability analysis of implicit deadline tasks under limited preemption EDF scheduling

Abstract

Limited-preemption forms of uniprocessor scheduling provide a practical trade-off between flexibility and system overheads in embedded kernels. This paper considers the limited-preemption scheduling of implicit deadline tasks using the EDF algorithm. Upper bounds for the occurrence of a deadline miss in these task sets are derived, and employed to create several sufficient schedulability tests of increasing complexity and tightness. Exact analysis is then considered, and an algorithm with polynomial-time complexity is developed for situations in which the CPU utilization is bounded to be less than unity. Experimentally, the sufficient tests are shown to have acceptance ratios increasing from ≈ 60% up to ≈ 99%, and the number of evaluated deadlines required for the exact test is reduced by several orders of magnitude over previously known techniques.

Limited Preemptive Scheduling for Real-Time Systems. A Survey

“…Under these assumptions, a task set is feasible with deferred preemptions only if the task set is feasible preemptively. The analysis of periodic tasks with floating nonpreemptive regions has also been developed under EDF [27], [28].…”

“…Defining as the blocking tolerance of the th job of after a critical instant, the schedulability of such a job can be checked using the following condition [31]: (26) where Hence, the blocking tolerance becomes (27) The blocking tolerance of task can be computed as the minimum blocking tolerance among the first jobs of in the longest Level-Active Period (28) where is defined in (3). From (27), it is easy to see that the blocking tolerances do not depend on , which can be set to without affecting the analysis.…”

A hybrid EDF algorithm for implementing resource-constrained real-time control applications

“…equa mallest) task pe p max (p min ) resp eemptive task is is the highe that the class med, i.e. a p e ability to l e e analysis that follows we adapt the techniques developed in [9] and [16] to produce a more efficient technique for hEDF analysis than the application of those in [9] alone. Before the describing the hEDF schedulability analysis, some definitions will be made.…”

“…The function (7) provides the same map between elapsed time and time available for scheduling non-preemptive tasks as that of the relationship t-f(t) in [9], but clearly is not recursive in nature (the evaluation of t np (t) does not explicitly require knowledge of t np (t-1), t np (t-2), … , t np (0)) and requires only O(n) for its evaluation on any particular input value of t. Since the preemptive task will never miss its deadline (given the trivial assumption that that c p < p p ), we can see that the task set is schedulable if and only if the following condition is satisfied ∀ ≥ 0 following the worst-case arrival of all tasks at t = 0 [7][9] [16]:…”

“…Given this bound, the algorithm presented in [16] may be modified to carry out the schedulability analysis by carrying out backwards iteration, starting from t', and checking the condition (8) until t reduces below d min . The algorithm is shown in pseudocode below, where an uppercase D is used to represent absolute deadlines of task instances, to distinguish from task relative deadlines.…”