Weakly-hard Real-time Guarantees for Earliest Deadline First Scheduling of Independent Tasks

Abstract

The current trend in modeling and analyzing real-time systems is toward tighter yet safe timing constraints. Many practical real-time systems can de facto sustain a bounded number of deadline-misses, i.e., they have Weakly-Hard Real-Time (WHRT) constraints rather than hard real-time constraints. Therefore, we strive to provide tight Deadline Miss Models (DMMs) in complement to tight response time bounds for such systems. In this work, we bound the distribution of deadline-misses for task sets running on uniprocessors using the Earliest Deadline First (EDF) scheduling policy. We assume tasks miss their deadlines due to transient overload resulting from sporadic jobs, e.g., interrupt service routines. We use Typical Worst-Case Analysis (TWCA) to tackle the problem in this context. Also, we address the sources of pessimism in computing DMMs, and we discuss the limitations of the proposed analysis. This work is motivated by and validated on a realistic case study inspired by industrial practice (satellite on-board software) and on a set of synthetic test cases. The synthetic experiment is dedicated to extensively study the impact of EDF on DMMs by presenting a comparison between DMMs computed under EDF and Rate Monotonic (RM). The results show the usefulness of this approach for temporarily overloaded systems when EDF scheduling is considered. They also show that EDF is especially well for WHRT tasks.

A Generic Coq Proof of Typical Worst-Case Analysis

“…Then, we can conclude that gdmmd τ (dt) ≤ dmm τ (dt). Applying the same reasoning used in Section III to convert a DMM over bounded intervals to a DMM for k-sequences and equation (19), we can conclude that dm σ τ (I) ≤ dmm τ (k) We have seen how to derive the state of the art TWCA from our generic proof. It also shows that the use of a more precise notion of combinations still allows us to pick a tradeoff between precision and scalability without rebuilding the whole theory.…”

“…A similar concept exists for other scheduling policies, e.g. Fixed Priority Non-Preemptive (FPNP) [26] and Earliest Deadline First (EDF) [19], but so far a separate proof is required to apply TWCA to these policies. What we show in the following is that a more general concept of analyzable window with a few key properties is sufficient to apply TWCA.…”

“…We outline here the required modifications to the response time analysis in [29] for the EDF scheduling policy to turn it into a local deadline miss analysis. In other words, we show how to systematically derive the result of [19], which introduces TWCA for EDF. We work under the same assumptions as the response time analysis and consider periodic tasks.…”

Average Task Execution Time Minimization under (m, k) Soft Error Constraint

“…Another series of fault tolerance techniques rely on the (m, k) models, which is originally developed for guaranteeing limited deadline misses for firmed real-time systems, or socalled weakly-hard real-time systems [4], where a task has to meet at least m deadlines, or can miss at most m deadlines, in any of k consecutive jobs 2 . Although the original work [4] applied n m to describe the any n of m, most of the following works utilize the (m, k) to describe the weakly-hard constraints [11], [18], [39], [43]. Afterwards, such (m, k) models are commonly applied for fault tolerance related domain as well to describe the robustness constraints of (control) systems.…”

“…That is, a task must have at least m correct jobs out of any k consecutive jobs. While the original concept of (m, k)-constraints [17] was designed for allowing limited deadline misses [11], [18], the concept of (m, k)-constraints is equally applicable to specify admissible limited numbers of soft errors.…”