Uniprocessor EDF Feasibility is an Integer Problem

The research on real-time scheduling has mostly focused on the development of algorithms that allows to test whether the constraints imposed on the task execution (often expressed by deadlines) are verified or not. However, in many design scenarios the task set is only partially known and these algorithms cannot be applied because they require the complete knowledge of all the parameters of the task set. Moreover, very often the designer has the freedom to select some of the task set parameters in order to maximize the system performance, and an arbitrary selection of the free parameters can lead either to poor performance or to a constraint violation. It is then useful to describe the feasibility region of the task set parameters by equations instead of by algorithms, so that optimization algorithms can be applied to find the best assignment to the free variables. In this paper we formulate the EDF schedulability on a single processor through a combination of linear constraints. We study the geometry of the feasibility region of task deadlines when computation times and periods are known.