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

Scheduling theory as it applies to hard real-time environments with precedence and strict periodicity constraints — environments where the failure to satisfy any constraint may have disastrous consequences [1], [2] — seems currently to be enjoying a renaissance. The most widely studied problems in this field concern periodic non-preemptive tasks for systems where data are collected throught captors and the control is performed throught actuators [3], [4]. The tasks corresponding to captors and actuators must satisfy a strict periodicity constraint. For reasons of consistency and predictability, we assume in this paper that all tasks are subject to this constraint. The domains considered here include automobiles, avionics, mobile robotics, telecommunications, etc. 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, when preemption is allowed, 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. In this paper, we address the scheduling problem of hard real-time systems composed of dependent, strictly periodic, preemptive tasks in the monoprocessor case. The strictly periodic constraint implies that, for such a system, any task starts its execution at the beginning of its period whereas the dependence constraint implies that any task cannot start its execution before the end of another task preceding it. We assume here that no jitter is allowed at the beginning of each task. To clearly distinguish between the specification level and its associated model, we shall use the term operation rather than the commonly used “task” [5] which is too closely related to the implementation level. For systems with the above-mentioned constraints, in [6] we proved that some of them can be eliminated because they are definitely not schedulable, then we solved the problem