Low latency replication coded storage over memory-constrained servers

We consider a distributed storage system storing a single file, where the file is divided into equal sized fragments. The fragments are replicated with a common replication factor, and stored across servers with identical storage capacity. An incoming download request for this file is sent to all the servers, and it is considered serviced when all the unique fragments are downloaded. The download time for all fragments across all servers, is modeled as an independent and identically distributed (i.i.d.) random variable. The mean download time can be bounded in terms of the expected number of useful servers available after gathering each fragment. We find the mean number of useful servers after collecting each fragment, for a random storage scheme for replication codes. We show that the performance of the random storage for replication code achieves the upper bound for expected number of useful servers at every download asymptotically in number of servers for any storage capacity. Further, we show that the performance of this storage scheme is comparable to that of Maximum Distance Separable (MDS) coded storage.