A Generalized Digraph Model for Expressing Dependencies

Abstract

In the context of computer assisted verification of schedulability analyses, very expressive task models are useful to factorize the correctness proofs of as many analyses as possible. The digraph task model seems a good candidate due to its powerful expressivity. Alas, its ability to capture dependencies between arrival and execution times of jobs of different tasks is very limited. We propose here a task model that generalizes the digraph model and its corresponding analysis for fixed-priority scheduling with limited preemption. A task may generate several types of jobs, each with its own worst-case execution time, priority, non-preemptable segments and maximum jitter. We present the correctness proof of the analysis in a way amenable to its formalization in the Coq proof assistant.Our objective (still in progress) is to formally certify the analysis for that general model such that the correctness proof of a more specific (standard or novel) analysis boils down to specifying and proving its translation into our model. Furthermore, expressing many different analyses in a common framework paves the way for formal comparisons.

CertiCAN certifying CAN analyses and their results

“…In particular, there may be several jobs of the same task activated in the same busy window. To provide a tighter bound on the response time of , we introduce the notions of phase and queueing delay, similar to their definition in [15]. Definition 3 (Queueing delay).…”

Self-Aware Scheduling for Mixed-Criticality Component-Based Systems

“…traces with a hyper-periodic sequence of execution times. There exists a large body of research looking at more exact digraph task models [16], [17] than the periodic task model. In the scope of this work, we use the execution time model (ET model) [18] that generalises such traces and that is comparatively low in complexity when it comes to implementation.…”

“…Precedence relations between tasks are reflected in task graphs of different expressiveness [16]. Yet, although these models may have a notion of limited preemptability [17], they rarely incorporate the non-reentrant nature of single-threaded address spaces that leads to blocking. Modelling precedence and blocking relations in real-time applications to perform response-time analyses has been addressed by MAST [29], which bases on MARTE UML [30].…”

CertiCAN: A Tool for the Coq Certification of CAN Analysis Results

“…We thus consider the response time of each level-k job in a level-k busy window. To this aim, we use the notions of phase and queueing prefix as defined in [15].…”