Guiding Simulations of Multi-Tier Storage Caches Using Knee Detection

Simulating storage cache hierarchies enables efficient exploration of their configuration space, including diverse topologies, parameters and policies, and devices with varied performance characteristics, while avoiding expensive physical experiments. Miss Ratio Curves (MRCs) efficiently characterize the performance of a cache over a range of cache sizes. These useful tools reveal “key points” for cache simulation, such as knees in the curve that immediately follow sharp cliffs. Unfortunately, there are no automated techniques for efficiently finding key points in MRCs, and the cross-application of existing knee-detection algorithms yields inaccurate results. We present a multi-stage framework that identifies key points in any MRC, for both stack-based (e.g., LRU) and more sophis-ticated eviction algorithms (e.g., ARC). Our approach quickly locates candidates using efficient hash-based sampling, curve simplification, knee detection, and novel post-processing filters. We introduce Z-Method, a new multi-knee detection algorithm that employs statistical outlier detection to choose promising points robustly and efficiently. We evaluate our framework against seven other knee-detection algorithms, using both ARC and LRU MRCs from 106 diverse real-world workloads, and apply it to identify key points in multi-tier MRCs. Compared to naive approaches, our framework reduces the total number of points needed to accurately identify the best two-tier cache hierarchies by an average factor of approximately
$5.5\times$
for ARC and
$7.7\times$
for LRU.