A distributed file server system has multiple data servers connected to stream data files continuously over a network to multiple clients. Data files are distributed across the data servers so that data blocks of the data files are stored at each of the data servers. A scheduler is located at each of the data servers to manage distributed portions of a schedule. Each data server sees a different portion of the schedule, but no one data server sees the whole schedule. The scheduler facilitates service of requested data streams from its corresponding data server according to a schedule portion that is available to the data server. The scheduler determines whether to insert a new data stream into the current slot it presently owns in its schedule portion, or to wait for a subsequent slot in the schedule based on a thrifty policy.