Download Time Analysis for Distributed Storage Codes with Locality and Availability.

Availability codes have recently been proposed to facilitate efficient retrieval of frequently accessed (hot) data objects in distributed storage systems. This paper presents techniques for analyzing the download time of systematic availability codes considering the Fork-Join scheme for data access. Specifically, we consider the setup in which requests arrive for downloading individual data objects, and each request is replicated (forked) to the systematic server containing the object and all of its recovery groups. For low-traffic regime, when there is at most one request in the system, we compute the download time in closed-form and compare it across systems with availability, maximum distance separable (MDS), and replication codes. We demonstrate 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, which makes exact analysis intractable due to state space explosion. Here, we present upper and lower bounds on the download time, and an M/G/1 queue approximation for several special cases of interest. Via extensive numerical simulations, we evaluate our bounds, and demonstrate that the M/G/1 queue approximation has a high degree of accuracy.