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Queueing network models of Zoned RAID system performance

Abigail Lebrecht

PhD Thesis
Imperial College London
January, 2010
Abstract

RAID systems are widely deployed, both as standalone storage solutions and as the building blocks of modern virtualised storage platforms. An accurate model of RAID system performance is therefore critical towards fulfilling quality of service constraints for fast, reliable storage.

This thesis presents techniques and tools that model response times in zoned RAID systems. The inputs to this analysis are a specified I/O request arrival rate, an I/O request access profile, a given RAID configuration and physical disk parameters. The primary output of this analysis is an approximation to the cumulative distribution function of I/O request response time. From this, it is straightforward to calculate response time quantiles, as well as the mean, variance and higher moments of I/O request response time. The model supports RAID levels 0, 01, 10 and 5 and a variety of workload types.

Our RAID model is developed in a bottom-up hierarchical fashion. We begin by

modelling each zoned disk drive in the array as a single M/G/1 queue. The service time is modelled as the sum of the random variables of seek time, rotational latency and data transfer time. In doing so, we take into account the properties of zoned disks. We then abstract a RAID system as a fork-join queueing network. This comprises several queues, each of which represents one disk drive in the array. We tailor our basic fork-join approximation to account for the I/O request patterns associated with particular request types and request sizes under different RAID levels. We extend the RAID and disk models to support bulk arrivals, requests of different sizes and scheduling algorithms that reorder queueing requests to minimise disk head positioning time. Finally, we develop a corresponding simulation to improve and validate the model. To test the accuracy of all our models, we validate them against disk drive and RAID device measurements throughout.

Keywords
Performance Modelling and Analysis
Stochastic Modelling
AESOP
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