In this paper, we formally describe real-time systems with an abstract scheduler using Kripke structures. This formalization allows us to refine the abstract scheduler in its terms. We illustrate this approach with a non-preemptive global fixed priority scheduler (NE-GFP). We also formulate a safety property for real time systems using linear temporal logic LTL. We implement our formalization of real-time systems with a NE-GFP scheduler in language Promela used in the SPIN verification tool and make experiments for proving or disproving the safety property to evaluate the effectiveness of our approach.