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Task period adaptations are often used to alleviate temporal overload conditions in real-time systems. Existing frameworks assume that only task periods are adjustable and that task deadlines remain unchanged at all times. This paper formally introduces a more general real-time task model where task deadlines, which are less than or equal to task periods, are functions of task periods. This tight coupling between task deadlines and task periods has been discussed in a recent work in control systems and presents a novel real-time scheduling challenge. To solve the period and deadline selection problem, this article identifies a feasible period-deadline combination and proposes a heuristic, which iteratively adjusts task periods and deadlines in such a way that the task set becomes schedulable. Experimental results show that the heuristic finds a solution to the period and deadline selection problem over 73% of the time, using less than three search iterations. When it is unable to find a solution to the problem, the heuristic requires less than 0.02s to run in the worst-case (with at most 100 search iterations).