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Distributed storage systems often employ erasure codes to achieve high datareliability while attaining space efficiency. Such storage systems are known tobe susceptible to long tails in response time. It has been shown that in modernonline applications such as Bing, Facebook, and Amazon, the long tail oflatency is of particular concern, with $99.9$th percentile response times thatare orders of magnitude worse than the mean. Taming tail latency is verychallenging in erasure-coded storage systems since quantify tail latency (i.e.,$x$th-percentile latency for arbitrary $x\in[0,1]$) has been a long-standingopen problem. In this paper, we propose a mathematical model to quantify {\emtail index} of service latency for arbitrary erasure-coded storage systems, bycharacterizing the asymptotic behavior of latency distribution tails. When filesize has a heavy tailed distribution, we find tail index, defined as theexponent at which latency tail probability diminishes to zero, in closed-form,and further show that a family of probabilistic scheduling algorithms are(asymptotically) optimal since they are able to achieve the exact tail index.

Tail Index for a Distributed Storage System with Pareto File Size Distribution