Practical Bounds on Optimal Caching with Variable Object Sizes

TL;DR

This paper introduces a flow-based method to compute tight bounds on the optimal caching miss ratio with variable object sizes, revealing the potential for significant improvements over current caching policies.

Contribution

The paper presents a novel flow-based approach (FOO) for accurately bounding the optimal caching performance with variable object sizes, and extends it to practical scenarios (PFOO) for large-scale traces.

Findings

FOO achieves less than 0.3% error on 10 million requests.

Current caching systems miss 11-43% more than the optimal.

Prior bounds suggested near-optimal performance, but FOO reveals significant room for improvement.

Abstract

Many recent caching systems aim to improve miss ratios, but there is no good sense among practitioners of how much further miss ratios can be improved. In other words, should the systems community continue working on this problem? Currently, there is no principled answer to this question. In practice, object sizes often vary by several orders of magnitude, where computing the optimal miss ratio (OPT) is known to be NP-hard. The few known results on caching with variable object sizes provide very weak bounds and are impractical to compute on traces of realistic length. We propose a new method to compute upper and lower bounds on OPT. Our key insight is to represent caching as a min-cost flow problem, hence we call our method the flow-based offline optimal (FOO). We prove that, under simple independence assumptions, FOO's bounds become tight as the number of objects goes to infinity. Indeed, FOO's error over 10M requests of production CDN and storage traces is negligible: at most 0.3%. FOO thus reveals, for the first time, the limits of caching with variable object sizes. While FOO is very accurate, it is computationally impractical on traces with hundreds of millions of requests. We therefore extend FOO to obtain more efficient bounds on OPT, which we call practical flow-based offline optimal (PFOO). We evaluate PFOO on several full production traces and use it to compare OPT to prior online policies. This analysis shows that current caching systems are in fact still far from optimal, suffering 11-43% more cache misses than OPT, whereas the best prior offline bounds suggest that there is essentially no room for improvement.