Distribution Fitting and Performance Modeling for Storage Traces

Abstract

Understanding I/O workloads and modeling their performance is important for optimizing storage systems. A useful first step towards understanding the characteristics of storage workloads is to analyze their inter-arrival times and service requirements. If these characteristics are found to follow certain probability distributions, then corresponding stochastic models can be employed to efficiently estimate the performance of storage workloads. Such approaches have been explored in other domains using an assortment of distributions, including the Normal, Weibull, and Exponential. However, our analysis and others' past attempts revealed that none of those distributions provided a good fit for storage workloads. We analyzed over 200 traces across 4 different workload families using 20 widely used distributions, including ones seldom used for storage modeling. We found that the Hyper-exponential distribution with just two phases H_2 was superior in modeling the storage traces compared to other distributions under five diverse metrics of accuracy, including metrics that assess the risk of over-fitting. Based on these results, we developed a Markov-chain-based stochastic model that accurately estimates the storage system performance across several workload traces. To highlight the applicability of our model, we conducted what-if analyses to investigate the performance impact of workload variability and garbage collection under various scenarios.