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Constructing runtime tasks, or operating system-level processes/threads, from the components of software design models is crucial to the model-based development of embedded control software. A better method should explore more design choices and reduce the overheads of the runtime system to meet the timing and resource constraints of embedded control software. This paper presents a novel, two-step method for systematic and automatic construction of runtime tasks from software design models. It uses graph transformation to construct a task set meeting system-level end-to-end (e2e) timing constraints. Its first step decomposes the system-level e2e timing constraints into the components' timing constraints, which form a necessary condition for any valid and feasible schedule. The second step iteratively merges the components into tasks and sequences their executions. A thus-constructed task set is proven to meet both intercomponent precedence and system-level e2e timing constraints and to minimize runtime overheads by minimizing the total number of resultant tasks. Our evaluation results based on randomly generated software models have shown that the proposed method outperforms commonly used methods and is also scalable.