Schedulability Analysis for non Necessarily Harmonic Real-Time Systems with Precedence and Strict Periodicity Constraints using the Exact Number of Preemptions and no Idle Time

In this report we study hard real-time systems composed of dependent strictly periodic preemptive tasks in the monoprocessor case. Although preemptive scheduling algorithms are able to successfully schedule some systems that cannot be scheduled by any non preemptive scheduling algorithm, the cost of preemption may not be negligible. Therefore, its exact cost has to be explicitly considered in the schedulability conditions in order to avoid wasting resources and provide safety in terms of guaranteeing the right behavior of the system at run-time. Because we are interested in hard real-time systems with precedence and strict periodicity constraints where it is mandatory to satisfy these constraints, we have already shown in a previous work how to tackle this problem for systems composed of harmonic tasks. Two main contributions are presented in this report. First, we generalize our previous results to the case of systems with periods that are not necessarily harmonic. Second, we provide a necessary and sufficient schedulability condition which takes into account the exact number of preemptions for a system with such constraints when no idle time is allowed.