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In grid computing environments, a resource control that considers not only the ability of computer resources but also available network resources is needed in order to execute parallel and distributed processing effectively. In particular, the execution performance of a grid application will sometimes decrease due to the congestion caused by multiple flows running on the same network path. Therefore, a network control scheme in grid computing environments should consider the multiple flows generated from its own application as well as from other applications. In this paper, we propose and evaluate its effect of a priority control scheme for multiple flows that are generated simultaneously, in order to reduce the execution time of the grid applications without reserving network resources. Moreover, a method for improving the effect of the priority control by using path selection is discussed, which distinguishes the priority flows from the other flows.