Distributed and peer-to-peer storage systems are foreseen as an alternative to the traditional data centers and in-house backup solutions. In the past few years many peer-to- peer storage systems have been proposed. Most of them rely on the use of erasure codes to introduce redundancy to the data. This kind of system depends on many parameters that need to be well tuned, such as the factor of redundancy, the frequency of data repair and the size of a data block. In this paper we give closed-form mathematical expressions that estimate the system average behavior. These expressions are derived from a Markov chain. Our contribution is a guideline to system designers and administrators to choose the best set of parameters. That is, how to tune the system parameters to obtain a desired level of reliability under a given constraint of bandwidth consumption. We confirm that a lazy repair strategy can be employed to amortize the repairing cost. Moreover, we propose a formula to calculate the optimal threshold value that minimizes the bandwidth consumption. Finally, we additionally discuss the impact of different system characteristics on the performance metrics, such as the number of peers, the amount of stored data, and the disk failure rate. To the best of our knowledge this is the first work to give close-form formulas to estimate the bandwidth consumption for a lazy repair, and the loss rate taking into account the repair time.
['Frédéric Giroire', 'Julian Monteiro', 'Stéphane Pérennes']
Peer-to-Peer Storage Systems: A Practical Guideline to be Lazy