Abstract—In hard real-time systems, each task must not only be functionally correct but also meet its timing constraints. A common approach to characterizing hard real-time tasks with repetitive requests is the periodic task model [1]. In the periodic task model, every task needs to be executed once during each of its periods. The execution of a task in one period is independent of the execution of the same task in another period. Hence, the executions of the same task in two consecutive periods may be right next to each other, or at the far ends of the two periods. While the periodic task model can serve as a simple paradigm for scheduling tasks with repetitive requests, it may not be suitable for all real-time applications. For example, in some real-time systems, the temporal distance between the finishing times of any two consecutive executions of the same task must be less than or equal to a given value. In other words, each execution of a task has a deadline relative to the finishing time of the previous execution of the same task. Scheduling algorithms designed for the periodic task model may not provide efficient solutions for tasks with temporal distance constraints.

In this paper, we propose the (preemptive) distance-constrained task system model which can serve as a more intuitive and adequate scheduling model for "repetitive" task executions. We design an efficient scheduling scheme for the model, and derive a schedulability condition for the scheduling scheme. The schedulability condition is a measure for providing the fundamental predictability requirement in hard real-time applications. To show the usefulness of the distance-constrained task model and its scheduling scheme, we also discuss how to apply the scheduling scheme to real-time sporadic task scheduling and to real-time communications.