A polynomial feasibility test for preemptive periodic scheduling of unrelated processors (Q1067785)

We consider the problem of preemptive scheduling a set of periodically occurring jobs on a set of unrelated processors, that is, processors having different speeds for different jobs. We assume that each occurrence of a job has to be completely processed before the next occurrence of the same job. We provide a system of linear inequalities for testing the existence of a feasible schedule which can be solved in polynomial time. We then use the solution of this linear system, if any, for constructing a feasible schedule in a straightforward way.