In this research, we extend the traditional model of recurrent real-time tasks to incorporate the cost of context switches; we introduce the concept of Non-Resumable delays (i.e., loading phases are preemptive, but the processing time already expended in attempting to load a task is forfeited). We propose a model that addresses previous methodology flaws regarding the pessimism and scheduling anomalies, which could be implementable on certain Real-Time Operating System (RTOS) and models high-level abstraction of what is a context switch activity. We provide two exact schedulability tests for two popular scheduling families (Fixed Task Priority as Rate Monotonic and Fixed Job Priority as Earliest Deadline First). These tests are sustainable regarding the execution times and the preemption costs. They are based on the notion of simulation interval and properties of the schedule repetition. We conclude with a discussion of the advantages and drawbacks of our model and the future perspectives it opens up.