The paper presents techniques for analyzing the expected download time in distributed storage systems that employ systematic availability codes. These codes provide access to hot data through the systematic server containing the object and multiple recovery groups. When a request for an object is received, it can be replicated (forked) to the systematic server and all recovery groups. We first consider the low-traffic regime and present the close-form expression for the download time. By comparison 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. In the high-traffic regime, the system consists of multiple inter-dependent Fork-Join queues, making exact analysis intractable. Accordingly, we present upper and lower bounds on the download time, and an M/G/1 queue approximation for several 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.
翻译：本文介绍了分析使用系统可用代码的分布式存储系统的预期下载时间的技术。 这些代码通过包含对象和多个回收组的系统服务器提供获取热数据的途径。 当收到对对象的请求时, 可以( 提前) 复制给系统服务器和所有回收组。 我们首先考虑低流量机制, 并展示下载时间的近形表达方式。 与可用性、 最大距离可分离( MDS) 和复制代码相比, 我们显示, 可用代码可以减少某些设置的下载时间, 但不总是最佳的。 在高流量系统中, 系统由多个互相独立的福克- Join 队列组成, 使得精确的分析难以处理。 因此, 我们提出下载时间的上下界限, 以及一些感兴趣的情况下的 M/ G/1 队列近似值。 广泛的数字模拟, 我们评估我们的界限, 并显示 M/ G/1 队列近似高度准确性 。
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