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The parallel downloading technology is expected to utilize broad bandwidth and fetch a file quickly, retrieving each piece from a different server in parallel. When users retrieve a file from mirror servers in parallel, it is important that the files on the mirror servers should be identical. We have already proposed a proxy system which can ensure the sameness of files for users. In this paper we combine the parallel downloading technology and the proxy server technology in order to download a file quickly and to serve the latest files. However, our original parallel downloading method proposed previously has taken neither the downloading order of pieces of a file nor the requirement for the buffer space into account. In order to provide users with the required file in order as a byte stream, the proxy server should reorder the pieces fetched from multiple servers and fill the delayed blocks in as soon as possible. Thus, "substituting download" is newly introduced, which requests the delayed block also from another server to complete downloading earlier. We have clarified a tradeoff between the buffering time and the redundant traffic generated by duplicate requests to multiple servers using the substituting download through experiments on the Internet. As a result, some adjustments to balance the tradeoff work well and our method are proved both to download a file fast and to limit the buffer space. This technology is to be used to ensure the reliable and swift services as network assurance systems.