Modeling Preemptive EDF and FP by Integer Variables

Abstract The design of any system can be modeled by an optimization problem, where a decision must be taken to maximize an overall utility function within some constraints (that can be physical, contractual, etc.). In hard real-time systems the constraints are specified by the deadlines that are set for the completion of tasks. However classic schedulability tests are formulated by algorithms that prevent a visualization of the feasible region of the designer choices. In this paper we formulate the EDF and FP exact schedulability conditions on a single processor through a combination of linear constraints. We believe that this alternate representation is better suited for optimization and can trigger the development of more effective design methodologies for real-time systems.