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 contains 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.

中文翻译：

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具有局部性和可用性的分布式存储代码的下载时间分析

本文介绍了在采用系统可用性代码的分布式存储系统中分析预期下载时间的技术。这些代码通过包含对象和多个恢复组的系统服务器提供对热数据的访问。当收到对象请求时，可以将其复制（分叉）到系统服务器和所有恢复组。我们首先考虑低流量状态并呈现下载时间的接近形式表达式。通过比较具有可用性、最大可分离距离 (MDS) 和复制代码的系统，我们证明可用性代码可以在某些设置中减少下载时间，但并不总是最佳的。在高流量状态下，系统包含多个相互依赖的 Fork-Join 队列，使得精确分析变得棘手。因此，我们给出了下载时间的上限和下限，以及几个感兴趣的案例的 M/G/1 队列近似值。通过广泛的数值模拟，我们评估了我们的界限并证明 M/G/1 队列近似具有高度的准确性。