In a real-time system, when the execution of a task is preempted by another task, the interrupted task falls into a blocked state. Since its re-execution begins from the interrupted point generally, the task's timer containing the remaining time until its completion should be maintained in the blocked state. This is the reason for introducing the notion of memorable events in this paper. We present a new timed discrete event model (TDEM) that adds the memorable events to the TDEM framework of Brandin and Wonham (1994). Using supervisory control theory upon the proposed TDEM, we analyze the schedulability of preemptable periodic and sporadic tasks executing on a uniprocessor.