Analyzing the Download Time of Availability Codes
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Availability codes have recently been proposed to facilitate efficient storage, management, and retrieval of frequently accessed data in distributed storage systems. Such codes provide multiple disjoint recovery groups for each data object, which makes it possible for multiple users to access the same object in a non-overlapping way. However in the presence of server-side performance variability, downloading an object using a recovery group takes longer than using a single server hosting the object. Therefore it is not immediately clear whether availability codes reduce latency to access hot data. Accordingly, the goal of this paper is to analyze, using a queuing theoretical approach, the download time in storage systems that employ availability codes. For data access, we consider the widely adopted Fork-Join model with redundancy. In this model, each request arrival splits into multiple copies and completes as soon as any one of the copies finishes service. We first carry out the analysis under the low-traffic regime in which case the system consists of at most one download request at any time. In this setting, we compare the download time in systems with availability, maximum distance separable (MDS), and replication codes. Our results indicate that availability codes can reduce download time in some settings, but are not always optimal. When the low-traffic assumption does not hold, system consists of multiple inter-dependent Fork-Join queues operating in parallel, which makes the exact analysis intractable. For this case we present upper and lower bounds on the download time. These bounds yield insight on system performance with respect to varying popularities over the stored objects. We also derive an M/G/1 queue approximation for the system, and show with simulations that it performs well in estimating the actual system performance.
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