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A task that suspends itself to wait for an I/O completion or to wait for an event from another node in distributed environments is called an I/O blocking task. In conventional hard real-time scheduling theories, there exist several approaches to schedule such I/O blocking tasks within the conventional framework of rate monotonic analysis (RMA). However, most of them are pessimistic. In this paper, we propose effective algorithms that can schedule a task set which includes I/O blocking tasks under dynamic priority assignment. We present a new critical instant theorem for multi-frame task set under dynamic priority assignment. The schedulability is analyzed under the new critical instant theorem. For the schedulability analysis , this paper presents saturation summation which is used to calculate maximum interference function (MIF). With the saturation summation, the schedulability of a task set including I/O blocking tasks can be analyzed more accurately. We propose an algorithm which is based on a frame laxity monotonic scheduling (FLMS). Genetic algorithm is also applied. From our experiments, we can conclude that the FLMS can significantly reduce the time of the calculation time, and GA can improve task schedulability ratio than the FLMS.