Philippe Robert - Asymptotic Studies of Large Distributed systems with Failures

The qualitative behavior of a large scale storage network of non reliable file servers is investigated. In such systems a fraction of the processing capacity can be used to duplicate files on new servers when necessary. Due to random losses, with probability 1 all files will be lost eventually if no new files are added. The main question in this context is of understanding the relation between the durability of the system and the parameters of the network: the duplication capacity, the failure rate, the duplication factor and the average load of a node. Different scalings via mean-field limits or stochastic averaging can be used to study the eventual decay of these networks. They will be reviewed and discussed. An analysis of placement algorithms will be also presented.