Section: New Results

Uniprocessor Real-Time Scheduling

Participants : Laurent George, Mohamed Marouf, Daniel De Rauglaudre, Yves Sorel.

Combination of Non-Preemptive and Preemptive Tasks

We focused on fixed priority scheduling for a combination of non-preemptive strict periodic tasks in conjunction with preemptive sporadic tasks, that we extended to software fault tolerance [29] . We first investigated the transient phase for non-preemptive strict periodic tasks and we proved that its length is smaller than the transient phase for preemptive periodic tasks. Then, we determined the worst case scenario for preemptive sporadic tasks where the Worst Case Response Time (WCRT) can be obtained in the presence of strict periodic tasks. We proved that these release times belong only to the permanent phase of strict periodic tasks, and thus that the schedulability analysis for sporadic tasks can be restricted to the permanent phase. For preemptive sporadic tasks, we extended the classical necessary and sufficient schedulability condition based on the worst case response time computation to take into account non-preemptive strict periodic tasks. Finally, we considered software fault tolerance in the particular case where each primary strict periodic task has an alternate sporadic task which is released when the primary task fails. The schedulability analysis guarantees that even if all strict periodic tasks fail then all their respective alternate tasks will meet their deadlines.

Formal Proofs of Real-Time Scheduling Theorems

We completed two formal proofs of theorems in Coq on scheduling of fixed priority real-time preemptive tasks: one dealing with the sizes of busy periods (about 3500 lines of Coq), and another one dealing with response time (about 5200 lines of Coq). A monograph about these proofs, together with the formal check in Coq of scheduling conditions of strict periodicity, presented in the conference JFLA 2012 [37] , have been started (currently about 70 pages).