Repair Time in Distributed Storage Systems

In this paper, we analyze a highly distributed backup storage system realized by means of nano datacenters (NaDa). NaDa have been recently proposed as a way to mitigate the growing energy, bandwidth and device costs of traditional data centers, following the popularity of cloud computing. These service provider-controlled peer-to-peer systems take advantage of resources already committed to always-on set top boxes, the fact they do not generate heat dissipation costs and their proximity to users. In this kind of systems redundancy is introduced to preserve the data in case of peer failures or departures. To ensure long-term fault tolerance, the storage system must have a self-repairing service that continuously reconstructs the fragments of redundancy that are lost. The speed of this reconstruction process is crucial for the data survival. This speed is mainly determined by how much bandwidth, which is a critical resource of such systems, is available. In the literature, the reconstruction times are modeled as independent (e.g., poissonian, deterministic, or more generally following any distribution). In practice, however, numerous reconstructions start at the same time (when the system detects that a peer has failed). Consequently, they are correlated to each other because concurrent reconstructions do compete for the same bandwidth. This correlation negatively impacts the efficiency of the bandwidth utilization and henceforth the repair time. We propose a new analytical framework that takes into account this correlation when estimating the repair time and the probability of data loss. Mainly, we introduce a queuing model in which reconstructions are served by peers at a rate that depends on the available bandwidth. We show that the load is unbalanced among peers (young peers inherently store less data than the old ones). This leads us to introduce a correcting factor on the repair rate of the system. The models and schemes proposed are validated by mathematical analysis, extensive set of simulations, and experimentation using the GRID5000 test-bed platform. This new model allows system designers to operate a more accurate choice of system parameters in function of their targeted data durability. ? The research leading to these results has received funding from the European Project FP7 EULER, ANR CEDRE, ANR AGAPE, Associated Team AlDyNet, project ECOS-Sud Chile and région PACA. 2 Authors Suppressed Due to Excessive Length