Generalized Weakly Hard Schedulability Analysis for Real-Time Periodic Tasks

Abstract

The weakly hard real-time model is an abstraction for applications, including control systems, that can tolerate occasional deadline misses, but can also be compromised if a sufficiently high number of late terminations occur in a given time window. The weakly hard model allows us to constrain the maximum number of acceptable missed deadlines in any set of consecutive task executions. A big challenge for weakly hard systems is to provide a schedulability analysis that applies to a general task model, while avoiding excessive pessimism. In this work, we develop a general weakly hard analysis based on a Mixed Integer Linear Programming (MILP) formulation. The analysis applies to constrained-deadline periodic real-time systems scheduled with fixed priority and no knowledge of the task activation offsets, while allowing for activation jitter. Our analysis considers two common policies for handling missed deadlines, i.e., (i) letting the job continue until completion or (ii) killing its execution immediately. For this policy, ours is the first and only m-k analysis currently available. Experiments conducted on randomly generated task sets show the applicability and accuracy of the proposed technique as well as the improvements with respect to competing techniques.

Integrating I-DEVS and schedulability methods for analyzing real-time systems constraints

“…46 This solution guarantees that the applications meet their deadlines, and it works to minimize the global execution time. A generalized weakly hard analysis of real-time on uniprocessor systems for limiting the number of deadline misses is proposed in Pazzaglia et al 47 Our solution is based on the principle of the EDF scheduling, priority-driven, and imprecise computation with the mandatory-first approach to integrate I-DEVS with schedulability analysis approaches. In Section 3, we introduce the I-DEVS schedulability model based on the definition of WCET, and in Section 4 we present the I-DEVS schedulability formulation based on the definition of WRT.…”

“…46 This solution guarantees that the applications meet their deadlines, and it works to minimize the global execution time. A generalized weakly hard analysis of real-time on uniprocessor systems for limiting the number of deadline misses is proposed in Pazzaglia et al 47…”

Stability of Control Systems under Extended Weakly-Hard Constraints

“…A task τ may satisfy any combination of these four basic weakly hard constraints: The model expressed in (ii) was first introduced in [18], but its complementary version (i) has gained most research traction recently, and is often referred to as the (m, k) model. In particular, schedulability analyses have been developed for the (m, k) model [20], [39]. Furthermore, a weakly-hard sensitivity analysis is implemented in a toolchain that allows to derive the strongest satisfied (m, k) constraint from C code [33].…”

“…[37]- [39], the most important being kill, skip-next, and queue (also denoted as continue). In particular, the results of [7], [32], [37] suggest that the Queue strategy (i.e., letting each job executing until completion, queuing newly released jobs) may create chain effects of missed deadlines, negatively affecting stability and performance.…”

“…There is however quite a mismatch between the guarantees that can be obtained for real-time tasks and platforms [9], [19], [20], [39], and the analysis that is available for control tasks [32], [38]. In particular, few works deal with the stability analysis of real-time control tasks subject to deadline misses, and they often lack generality.…”