LRU缓存的资源池化与分离
On Resource Pooling and Separation for LRU Caching
摘要：
使用最近最少使用（LRU）原则的缓存系统现在已经变得无处不在。这些系统的一个基本问题是，缓存空间是否应该集中在一起或划分，以服务于多个数据项请求流，以最大限度地减少未命中概率。在本文中，我们表明，这个问题没有直接的是或不是答案，这取决于关键因素的复杂组合，包括，例如，请求速率、跨不同请求流的重叠数据项、数据项流行度及其大小。具体来说，我们的特点是渐近错过概率多个竞争的请求流下的资源池和分离LRU缓存时，缓存大小是大的。分析上，我们表明，它是渐近最优的，共同服务多个流，如果他们的数据项的大小和流行度分布是相似的，他们的到达率没有显着差异; LRU缓存的自组织属性自动优化它们之间的资源分配渐近。否则，分离这些流可能会更好，例如，当数据大小变化很大时。我们还量化了临界点，超过这个临界点，当重叠的数据项超过一定的水平时，资源池比每个流的分离更好。从技术上讲，我们推广了现有的结果的LRU缓存的渐近错过概率为广泛的一类重尾分布，并将其扩展到多个竞争流与不同的数据项大小，这也验证了切近似在一定条件下。这些结果为提高缓存系统的性能提供了新的见解。
英文摘要：
Caching systems using the Least Recently Used (LRU) principle have now become ubiquitous. A fundamental question for these systems is whether the cache space should be pooled together or divided to serve multiple flows of data item requests in order to minimize the miss probabilities. In this paper, we show that there is no straight yes or no answer to this question, depending on complex combinations of critical factors, including, e.g., request rates, overlapped data items across different request flows, data item popularities and their sizes. Specifically, we characterize the asymptotic miss probabilities for multiple competing request flows under resource pooling and separation for LRU caching when the cache size is large. Analytically, we show that it is asymptotically optimal to jointly serve multiple flows if their data item sizes and popularity distributions are similar and their arrival rates do not differ significantly; the self-organizing property of LRU caching automatically optimizes the resource allocation among them asymptotically. Otherwise, separating these flows could be better, e.g., when data sizes vary significantly. We also quantify critical points beyond which resource pooling is better than separation for each of the flows when the overlapped data items exceed certain levels. Technically, we generalize existing results on the asymptotic miss probability of LRU caching for a broad class of heavy-tailed distributions and extend them to multiple competing flows with varying data item sizes, which also validates the Che approximation under certain conditions. These results provide new insights on improving the performance of caching systems.
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