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.

Computing the minimum edf feasible deadline in periodic systems

In most real-time applications, deadlines are artifices that need to be enforced to meet different performance requirements. For example, in periodic task sets, jitter requirements can be met by assigning suitable relative deadlines and guaranteeing the feasibility of the schedule. This paper presents a method (called minD) for calculating the minimum EDF-feasible deadline of a real-time task. More precisely, given a set of periodic tasks with hard real-time requirements, which is feasible under EDF, the proposed algorithm allows computing the shortest deadline that can be assigned to an arbitrary task in the set, or to a new incoming task (periodic or aperiodic), still preserving the EDF feasibility of the new task set. The algorithm has a pseudo polynomial complexity and handles arbitrary relative deadlines, which can be less than, equal to, or greater than periods. 1