Uniprocessor EDF Feasibility is an Integer Problem

Abstract

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.