A New Upper Bound on Cache Hit Probability for Non-Anticipative Caching Policies

Abstract

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 and 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. When object request processes are conditionally independent, we prove that this cache allocation based on the HR-to-size ratio rule guarantees the maximum achievable expected number of object hits across all non-anticipative caching policies. Further, the HR ordering rule serves as an upper bound on cache hit probability when object request processes follow either independent delayed renewal process or a Markov modulated Poisson process. We also derive closed form expressions for the upper bound under some specific object request arrival processes. We provide simulation results to validate its correctness and to compare it to the state-of-the-art upper bounds, such as produced by Bélády’s algorithm. We find it to be tighter than state-of-the-art upper bounds for some specific object request arrival processes such as independent renewal, Markov modulated, and shot noise processes.