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Under a competitive grid environment, the time delay involved in assigning resources can ruin the smooth execution of a highly interactive application with dynamic resource requirements. To solve this problem, we propose two novel approaches to be embedded on top of the generic resource management. One approach is the priority-based allocation policy that gives advantages for the urgent requests; another is the resource permit swapping policy that is proposed to resolve resource requirements conflicts. Experimental results and analyses demonstrate the effectiveness of our approach in terms of the satisfaction of urgent requests in maintaining the smooth time progression for highly dynamic applications and also the satisfaction of other types of applications.