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In a future ubiquitous computing environment, server computers will exist everywhere and thus mobile computer users can take services from their nearest server even when their mobile computers do not have enough resources such as CPU power and storage. In such an environment, however, a wide range of network resources is needed for communication between the mobile user and the server computer providing services if the user goes away from the server computer. To overcome this problem, a new process migration mechanism has been proposed, which can reduce network load and latency by transferring processes to the moving user's nearest server computer. The proposed mechanism can transfer processes to the right server computer before the user arriving by predicting a subsequent route of the moving user. The efficiency of the proposed mechanism is shown through case study.