一个新的非预期缓存命中概率上界
A New Upper Bound on Cache Hit Probability for Non-anticipative Caching Policies
摘要：
高速缓存系统长期以来对于提高各种网络和基于web的在线应用的性能至关重要。在这样的系统中，端到端应用程序的性能很大程度上取决于从缓存传输的对象的分数，也称为缓存命中概率。许多缓存策略已经被提出和实现，以提高命中概率。在这项工作中，我们提出了一种新的方法来计算所有非预期缓存策略的命中概率上限，即，对于不了解未来请求的策略。我们的关键见解是根据其危险率（HR）函数值与其大小的比率对对象进行排序，并将具有最大比率的对象放置在缓存中，直到缓存容量耗尽。在一些统计假设下，我们证明了我们提出的HR大小比为基础的排序模型计算的最大可实现的命中概率，并作为所有非预期缓存策略的上限。我们推导出一些特定的对象请求到达过程下的上界的封闭形式的表达式。我们还提供了仿真结果来验证其正确性，并将其与最先进的上界进行比较。我们发现它比各种对象请求到达过程的最先进的上限更紧。
英文摘要：
Caching systems have long been crucial for improving the performance of a wide variety of network and web based online applications. In such systems, end-to-end application performance heavily depends on the fraction of objects transferred from the cache, also known as the cache hit probability. Many caching policies have been proposed and implemented to improve the hit probability. In this work, we propose a new method to compute an upper bound on hit probability for all non-anticipative caching policies, i.e., for policies that have no knowledge of future requests. Our key insight is to order the objects according to the ratio of their Hazard Rate (HR) function values to their sizes and place in the cache the objects with the largest ratios till the cache capacity is exhausted. Under some statistical assumptions, we prove that our proposed HR to size ratio based ordering model computes the maximum achievable hit probability and serves as an upper bound for all non-anticipative caching policies. We derive closed form expressions for the upper bound under some specific object request arrival processes. We also provide simulation results to validate its correctness and to compare it to the state-of-the-art upper bounds. We find it to be tighter than state-of-the-art upper bounds for a variety of object request arrival processes.
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