一致性哈希下LRU缓存的渐近丢失率
Asymptotic Miss Ratio of LRU Caching with Consistent Hashing
摘要：
为了有效地扩展数据缓存基础设施以支持新兴的大数据应用，许多缓存系统依赖于一致性哈希来将大量服务器分组以形成协作集群。这些服务器根据随机哈希函数组织在一起。它们共同提供了一个统一但分布式的哈希表，以服务于快速和大量的数据项请求。不同于已经被广泛研究的单个最近最少使用（LRU）服务器，理论上表征由多个LRU服务器组成的集群仍然有待探索。这些服务器不是简单地加在一起;随机哈希使行为复杂化。为此，我们推导出的数据项请求的LRU集群一致性哈希的渐近未命中率。我们表明，这些不同的服务器上的个人缓存空间可以有效地被视为，如果他们可以汇集在一起，形成一个单一的虚拟LRU缓存空间参数化的适当的缓存大小。在各个服务器的高速缓存大小很大的条件下，可以严格地建立这种等价性。对于典型的数据缓存系统，这种情况很常见。我们的理论框架提供了一个方便的抽象，可以直接应用结果从简单的单个LRU缓存到更复杂的LRU集群一致的哈希。
英文摘要：
To efficiently scale data caching infrastructure to support emerging big data applications, many caching systems rely on consistent hashing to group a large number of servers to form a cooperative cluster. These servers are organized together according to a random hash function. They jointly provide a unified but distributed hash table to serve swift and voluminous data item requests. Different from the single least-recently-used (LRU) server that has already been extensively studied, theoretically characterizing a cluster that consists of multiple LRU servers remains yet to be explored. These servers are not simply added together; the random hashing complicates the behavior. To this end, we derive the asymptotic miss ratio of data item requests on a LRU cluster with consistent hashing. We show that these individual cache spaces on different servers can be effectively viewed as if they could be pooled together to form a single virtual LRU cache space parametrized by an appropriate cache size. This equivalence can be established rigorously under the condition that the cache sizes of the individual servers are large. For typical data caching systems this condition is common. Our theoretical framework provides a convenient abstraction that can directly apply the results from the simpler single LRU cache to the more complex LRU cluster with consistent hashing.
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