With a striped RAID (Redundant Array of Independent Disks) which consists of multiple disks and spreads data across them in parallel, distributed file systems (DFSs) easily enhance the performance of a single read stream (i.e., a series of sequential reads by a process). However, most existing DFSs suffer from performance degradation in concurrent read streams (i.e., multiple series of sequential reads by concurrent processes). Furthermore, research on the performance of concurrent ones for a striped RAID in DFSs has been rarely reported so far. In this paper, we define the problems that degrade it at different configurations of striped RAIDs, and resolve them by proposing the following two methods: (1) a fair allocating of network bandwidth for concurrent read streams and (2) a strip-aware prefetching for each individual read stream. We show that our proposal outperforms all the existing DFSs by at least two times for all kinds and configurations of striped RAIDs. Furthermore, the performance gap between our proposal and the existing DFSs becomes wider according to the increasing number of striped disks.