In this paper, we address the problem of scheduling periodic, possibly self-suspending, real-time tasks. We show how to use model checking to obtain both a necessary and sufficient feasibility test, and a schedulability test for classical scheduling policies (RM, DM, EDF). When these algorithms fail to schedule a feasible system, we show how to generate an appropriate scheduler. We provide also a method to test the sustainability of a schedule w.r.t execution and suspension durations. Finally, using a model checking tool we validate our approach.