Abstract
In this paper definitions for time constraints of steps of a real-time task (RTT) are presented. These definitions were constructed using set theory and functions theory and provided the basis for formalizing the concept of scheduler of tasks as a function that maps from the arrival times set to the start times set on a set of concurrent RTT. This definition is valid for any scheduler and its description does not depend of the scheduling algorithm or of the arrival time of the tasks. As an application, a study on the Rate Monotonic scheduler in which a specific case with time constraints is presented. The set of definitions will allow performing studies of stability, functionality, optimization, feasibility and comparison with other schedulers.
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