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A unified strategy for dynamic mapping in grid computing environments is brought forward. Immediate mode and batch mode are symbiotic and can switch adaptively in our strategy. It uses MCT for the immediate mode mapping and an improved sufferage algorithm, called utility-sufferage for the batch mode scheduling which the utility functions are defined to assure diverse QoS demands of tasks. The experimental results indicate that the improved scheme can achieve higher performances than the benchmark algorithms subject to varying task flow in grid computing environments.